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Интернет-журнал Науковедение

Вывод формулы связи энергии и частоты в макрои микромеханике

Кочетков Андрей Викторович, Федотов Петр Викторович, Шашков Игорь Геннадиевич, Ермолаева Вероника Викторовна

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

In article it is declared that creation of nuclear physics if will require new laws, any new representations it isn''t required. In Einstein''s formula anything quantum in the received formula isn''t present, and there is only a linear dependence of energy of fluctuations on frequency. For creation of classical nuclear physics and acceptance of postulates of Pine forest, but any more as empirical postulates and as normal classical laws of physics, aren''t present need to change any representations (as it it is taught now), and it is enough to adopt as the fact only two laws distinguishing macromechanics and micromechanics, but not contradicting classical physics. Gravitational waves (gravitational photons) don''t exist, and, the second, the kinetic moment of an impulse of orbital movement of electrons in atom has always one and too value, unlike a similar constant in the Newtonian mechanics. In all the rest nuclear mechanics differs nothing from usual Newtonian.

Related papers

Modern Physics and Nuclear Physics 2019: Atomic physics as the basis of quantum mechanics - Peter Enders - Taraz State Pedagogical University

P. Enders

Quantum physics begun with discretising the energy of resonators (Planck 1900). Quantum systems exhibit a substantially smaller amount of stationary states than classical systems (Einstein 1907). Planck’s and Einstein’s worked within statistical physics and electromagnetism. The first step toward quantum mechanics was, perhaps, Bohr’s 1913 atom model. The task was to explain the stability of the atoms and the frequencies and intensities of their spectral lines. Two of these three tasks concern stationary properties. Heisenberg’s 1925 matrix mechanics mastered them through a radical “reinterpretation of kinematic and mechanical relations”, where that article tackles the harmonic oscillator. The Bohr orbitals result directly from Schrodinger’s 1926 wave mechanics, though the discretisation method is that of classical resonators. The reuse of the classical expressions for the kinetic and potential energies needs justification. Without that, the tunnel effect remains a mystery provided that justification through an axiomatic deduction of the stationary and time-dependent Schrodinger equations from Euler‘s and Helmholtz’s rather than Newton’s and Hamilton’s representations of classical mechanics. Referring to Einstein, the stationary quantum states are selected out of the classical continuum not through the classical eigenvalue method, but using the intrinsic discreteness of the stationary Schrodinger equation and energy conservation. Unbound states are naturally included. The effective potential energy is always smaller than the total energy; a quantum particle does not ‘tunnel’ through a barrier, but jumps over a hill. The smooth transition from classical to quantum mechanics facilitates to teach and understand the latter one. One can give decent details why reality cannot at all be represented by a continuous field. From the Quantum phenomena it appears to follow with certainty that a finite system of finite energy can be completely described by a finite set of numbers (quantum numbers). This does not seen to be in accordance with a continuum theory and must lead to an attempt to find a purely algebraic theory of or the description of reality. It leads to the insight that, if gravity is a fundamental interaction and Quantum Mechanics is universally valid, the gravitational field will have to be quantized, not at least because of the inconsistency of semi-classical theories of gravity. The quantization must be adroitly sufficient, which implies specifically that the subsequent quantum hypothesis must be foundation autonomous. This can't be accomplished by methods for quantum field hypothetical procedures. The goal of a hypothesis of Quantum Gravity would then be to recognize the quantum properties and the quantum elements of the gravitational field. If this means to quantize General Relativity, the general-relativistic identification of the gravitational field with the space time metric has to be taken into account. The quantization must be reasonably sufficient, which implies specifically that the subsequent quantum hypothesis must be foundation free. This can't be accomplished by methods for quantum field hypothetical techniques. One of the fundamental prerequisites for such a quantization technique is, that the subsequent quantum hypothesis has a traditional breaking point that is (in any event roughly, and up to the known phenomenology) indistinguishable from General Relativity. Be that as it may, should gravity not be an essential, yet an incited, lingering, developing connection, it could in all likelihood be an inherently old style marvel. Should Quantum Mechanics be regardless generally substantial, we needed to expect a quantum substrate from which gravity would result as a new traditional marvel. What's more, there would be no contention with the contentions against semi-old style hypotheses, in light of the fact that there would be no gravity at all on the substrate level. The gravitational field would not have any quantum properties to be caught by a hypothesis of Quantum Gravity, and a quantization of General Relativity would not prompt any principal hypothesis. The target of a hypothesis of 'Quantum Gravity' would rather be the ID of the quantum substrate from which gravity results. The requirement that the substrate theory has General Relativity as a classical limit – that it reproduces at least the known phenomenology – would remain. The paper tries to give an overview over the main options for theory construction in the field of Quantum Gravity. Because of the still unclear status of gravity and space time, it pleads for the necessity of a plurality of conceptually different approaches to Quantum Gravity. The most essential motivations for the development of a theory of Quantum Gravity are generally supposed to be based on two (probably interrelated) types of problems(i) the mutual conceptual incompatibility between General Relativity on the one hand and Quantum Mechanics and Quantum Field Theory on the other hand.

Journal of Lasers Optics & Photonics•Jan 1, 2020•0 citations

The Cornerstones of Modern Physics

Koh Aik Khoon

This paper takes a look at the two cornerstones of modern physics--Quantum Mechanics and The Theory of Relativity (Both Special and General). The differences and similarities for the two subjects are presented. More of their differences and similarities will emerge with new developments in physics. One can't rule out the possibility of the two being unified into one one fine day. That will herald another triumphant moment in physics. Introduction In 1905, Albert Einstein at the age of twenty-six formulated single-handedly, among others, the Theory of Special Relativity together with his other seminal papers on photoelectricity, Brownian motions of atoms and molecular dimensions. The year has been universally declared the Miraculous Year [1]. Ten years later, he came up with the theory of General Relativity--a new and revolutionary framework on gravity. Meanwhile in Europe a group of young physicists played pivotal role in the birth of Quantum Mechanics. Many of them went on to win Nobel prizes for their monumental contributions. Einstein also won the coveted prize not for Relativity but ironically for Photoelectric Effect. Irony has been part of physics in its history. Relativity with its weird 'Twin Paradox', constancy of the speed of light and the interchangebility between mass and energy (E=[mc.sup.2]) enthralls the public and scientists alike. It provides a way to measure particle masses [2]. The Quantum Theory has its fair share of weirdness and bewilderment. Both Quantum Mechanics and the Theory of Relativity bring forth new ideas in human thoughts. They are among Joanne Baker's 50 physics ideas [3]. Quantum Mechanics and the Theory of Relativity The quantum world where counterintuition reigns supreme is couched in uncertainty as epitomised by Heisenberg's uncertainty principle. Things do not behave in a deterministic way as enshrined and expected in classical Newtonian physics. The microscopic world of the electrons was dictated by randomness and indeterminacy. Albert Einstein was appalled by such dictates that he famously declared: 'God does not play dice with the universe.' The famous Danish physicist Neils Bohr sprang to his feet by saying: 'Stop telling God what to do with his dice.' The sparring between the two stalwarts in physics is legendary. According to Trefil [4], there are a couple of things that need to be said about the uncertainty principle: it does not imply that we cannot know either the position or the velocity of a particle, and it does not require the presence of a conscious mind. Marcus Chown [5] wraps up by saying 'The bitter irony, not lost on Einstein, was that he was the one who, by postulating the existence of the photon, had inadvertently set loose the genie of randomness of physics. The two theories of relativity by Einstein are not couched in randomness however. According to Smoot [6], both implied a radically new cosmology. Many people are of the opinion that with Einstein's theory of relativity, old classical physics is no more in vogue. According to Angier [7], Albert Einstein did not prove that Isaac Newton was wrong. Instead, he showed that Newton's theories of motion and gravity were incomplete, and that new equations were needed to explain the behavior of objects under extreme circumstances, such as when tiny particles travel at or near the speed of light. …

College student journal•Sep 1, 2011•0 citations

A Link Merges Classical Mechanics to Quantum Theory (Part II)

Alaa S. Bayoumi

This article is a continuation of Part(I) to demonstrate more aspects for a successful merge of classical mechanics to the quantum theory. The article starts first with the deduction of the general form of the complimentary energy, next a robust firm mathematical proof is given indicates that the complimentary energy has a wave nature and it is a potential energy, then the radiation condition has been determined, a vector formula expresses the corresponding force was deduced and this force was called adhesion force. A mathematical convergence process has proved the duality of the electromagnetic wave parameters and particle parameters, which results in the existence of a “wave-particle” object. While finding the relationship between the electromagnetic wave parameters and particle parameters, a mathematical relationship was found indicating that not every moving charged mass generates a magnetic field. This relationship for the mass was linked to the effective mass tensor, The geometric representation of the constant energy surface and its relationship to the energy levels of both the orbital model (Bohr model) and the cloud model for different geometric 3D shapes were investigated as a sample of the possible geometric interpretations of the energy equation, that is by employing the triangle method, it is possible to create a geometric representation of the constant energy surfaces. The relation between the energy levels, quantum numbers, and band width is represented geometrically. As a result of proving the relationship between the motion of an electromagnetic wave and the motion of a particle associated with the wave, two new, unprecedented mathematical formulas were developed. The first formula specifies a moving charged mass and its relationship to the resulting wavelength. Thus, the radius of the charged mass is obtained in terms of its wavelength and mass density. The second formula specifies the kinetic energy of a photon. The grand potentials are the potential energy of the Newton’s Law of Universal Gravitation, Coulomb’s Law, and Inverse Square Law of Electromagnetic Waves Intensity. From the potential energy of Newton’s law of universal gravitation, the wavelength of the gravitational wave, as well as the wavelength of quantum gravity were deduced. A mathematical relationship was then deduced that determines the lengths of the functions of conic sections, and in particular the length of perimeter of ellipses. From the potential energy of Coulomb’s law of attraction, a mathematical formulation of the energy levels in general for any atom of an element was obtained. This mathematical formulation was compared with the results obtained by Bohr and Schrödinger for the hydrogen atom. As for the inverse square law of electromagnetic radiation intensity, several innovative mathematical equations have been deduced that link different parameters together. Following the contents of this article requires to be quite familiar with the contents of the first part with the same title, as well as a complete understanding of the concepts of intermediate parameters derived and used in the various equations. Otherwise, it will be extremely difficult to follow the contents of this article.

Journal of Applied Mathematics and Physics•Jan 1, 2025•1 citation

Пространство: относительность неклассических представлений

К. В. Кочелаевская, В. В. Афанасьева

The paper discusses the vague and contradicting non-classical notions of relativity and quantum mechanics leading to the absence of unified space-time concepts in the natural science.

Вестник Саратовского государственного технического университета•Jan 1, 2012•0 citations

On Dielectric Constants and Magnetic Susceptibilities in the New Quantum Mechanics Part III—Application to Dia- and Paramagnetism

John Hasbrouck Van Vleck

1.General mathematical theory.---Modifications are given in the general derivation of the Langevin-Debye formula by means of quantum mechanics published in part I which are required by the moment now being magnetic rather than electric. The main additions are the appearance of a diamagnetic term, and allowance for the fact that the magnetic moment consists of two parts arising respectively from orbital electronic motions and from the electrons' internal spins. These parts cannot always be treated as rigidly coupled to form a "permanent" resultant moment. The Hamiltonian function used for the internal spin is that of a spherical top.2.Diamagnetism.---The writer's previous claim that Pauli's formula for the diamagnetic susceptibility can be applied to molecules as well as atoms is shown to be invalid because of the anomalous fact that the square of the angular momentum, unlike the average angular momentum, does not vanish even in $S$ states when there is more than one nucleus. Pauli's formula is instead an upper limit to the diamagnetism in non-monatomic molecules and is a good approximation when the Schr\"odinger wave function has nearly as much symmetry as in an atomic $S$ state.3.Paramagnetism of atoms.---Limiting values for the paramagnetic susceptibilities of atoms are $\ensuremath{\chi}=N\frac{[4s(s+1)+k(k+1)]{\ensuremath{\beta}}^{2}}{3kT}$ and $\ensuremath{\chi}=[\frac{N{g}^{2}j(j+1){\ensuremath{\beta}}^{2}}{3kT}]+N\ensuremath{\alpha}$ where $\ensuremath{\beta}$ is the Bohr magneton and $\ensuremath{\alpha}$ is a constant. These two formulas are rigorously applicable when the multiplet intervals are respectively very small or very large compared to $\mathrm{kT}$, and are valid regardless of whether the magnetic field is strong enough to change the quantization by producing a Paschen-Back effect. The formula for small multiplets yields susceptibilities slightly different from those given by Laporte and Sommerfeld's expression for this case, and is much simpler, as they overlooked the contribution of the portion of the magnetic moment which is perpendicular to the invariable axis.4.Paramagnetism of molecules.---The susceptibility is calculated on the basis of the Hund theory of molecular quantization. Formulas are given applicable to his couplings of type (a) and type (b) provided in the former the multiplet intervals are either very large or very small compared to $\mathrm{kT}$. The experimental susceptibilities for ${\mathrm{O}}_{2}$ and Cl${\mathrm{O}}_{2}$ are in accord with the assumption that the normal states are respectively $^{3}S$ and $^{2}S$ terms. In the particular case of $S$ terms the numerical results are the same in the atomic and molecular formulas, but, unlike previous theories, it is not necessary to suppose the orbits are as freely oriented in molecules as in atoms. Polyatomic molecules may have lower paramagnetic susceptibilities than diatomic ones because the dissymmetry causes large fluctuations in electronic angular momentum.5.Paramagnetism of nitic oxide.---Spectroscopists have recently found that the normal states of the NO molecule are $^{2}P$ terms separated by 120.9 ${\mathrm{cm}}^{\ensuremath{-}1}$. This permits an unambigous calculation of the susceptibility of NO which agrees with the experimental value within 1.5 per cent. Deviations from Curie's law are calculated which result from the doublet interval being comparable with $\mathrm{kT}$. These deviations should be detectable experimentally if the susceptibility of NO could be measured over a wide temperature range.

Physical Review•Apr 1, 1928•110 citations

On Quantum Physics without Schrödinger Equation

Xiao En Wang

In the early 20th century, Planck, Einstein, Bohr, Sommerfeld, and de Broglie became the pioneers of quantum physics. Because the Schrödinger equation used the wrong energy relationship, it misled people’s understanding of quantum theory. Newtonian mechanics and Leibniz dynamics are correct. But Newton’s first law was tampered with by the British mathematician Mott during his translation, which excluded uniform circular motion from inertia; Leibniz’s kinetic energy mυ2 was modified by French engineer Coriolis to an engineering approximation of mυ2/2. Hamilton mistakenly applied the approximate kinetic energy formula of Coriolis in engineering mechanics to the dynamic analysis in theoretical physics, and established an incorrect Hamiltonian energy equation. Schrödinger ignored Sommerfeld’s research on the constant velocity of electrons in atoms, υ = αc, and thus the constant momentum and constant kinetic energy of electrons. He expressed the constant kinetic energy term of electrons as an operator that hides the velocity variable, and established the wave equation based on the incorrect Hamiltonian energy relationship. The Schrödinger equation deals with the ground state of hydrogen atoms, where electrons die when they reach twice the Bohr radius, which contradicts the stable existence of atoms. The Schrödinger ‎equation has been around for almost a century, and the quantum physics of the new millennium ‎should be a new quantum physics without the Schrödinger equation.

Journal of Physics & Optics Sciences•Apr 25, 2025•0 citations
In article it is declared that creation of nuclear physics if will require new laws, any new representations it isn''t required. In Einstein''s formula anything quantum in the received formula isn''t present, and there is only a linear dependence of energy of fluctuations on frequency. For creation of classical nuclear physics and acceptance of postulates of Pine forest, but any more as empirical postulates and as normal classical laws of physics, aren''t present need to change any representations (as it it is taught now), and it is enough to adopt as the fact only two laws distinguishing macromechanics and micromechanics, but not contradicting classical physics. Gravitational waves (gravitational photons) don''t exist, and, the second, the kinetic moment of an impulse of orbital movement of electrons in atom has always one and too value, unlike a similar constant in the Newtonian mechanics. In all the rest nuclear mechanics differs nothing from usual Newtonian.
Quantum physics begun with discretising the energy of resonators (Planck 1900). Quantum systems exhibit a substantially smaller amount of stationary states than classical systems (Einstein 1907). Planck’s and Einstein’s worked within statistical physics and electromagnetism. The first step toward quantum mechanics was, perhaps, Bohr’s 1913 atom model. The task was to explain the stability of the atoms and the frequencies and intensities of their spectral lines. Two of these three tasks concern stationary properties. Heisenberg’s 1925 matrix mechanics mastered them through a radical “reinterpretation of kinematic and mechanical relations”, where that article tackles the harmonic oscillator. The Bohr orbitals result directly from Schrodinger’s 1926 wave mechanics, though the discretisation method is that of classical resonators. The reuse of the classical expressions for the kinetic and potential energies needs justification. Without that, the tunnel effect remains a mystery provided that justification through an axiomatic deduction of the stationary and time-dependent Schrodinger equations from Euler‘s and Helmholtz’s rather than Newton’s and Hamilton’s representations of classical mechanics. Referring to Einstein, the stationary quantum states are selected out of the classical continuum not through the classical eigenvalue method, but using the intrinsic discreteness of the stationary Schrodinger equation and energy conservation. Unbound states are naturally included. The effective potential energy is always smaller than the total energy; a quantum particle does not ‘tunnel’ through a barrier, but jumps over a hill. The smooth transition from classical to quantum mechanics facilitates to teach and understand the latter one. One can give decent details why reality cannot at all be represented by a continuous field. From the Quantum phenomena it appears to follow with certainty that a finite system of finite energy can be completely described by a finite set of numbers (quantum numbers). This does not seen to be in accordance with a continuum theory and must lead to an attempt to find a purely algebraic theory of or the description of reality. It leads to the insight that, if gravity is a fundamental interaction and Quantum Mechanics is universally valid, the gravitational field will have to be quantized, not at least because of the inconsistency of semi-classical theories of gravity. The quantization must be adroitly sufficient, which implies specifically that the subsequent quantum hypothesis must be foundation autonomous. This can't be accomplished by methods for quantum field hypothetical procedures. The goal of a hypothesis of Quantum Gravity would then be to recognize the quantum properties and the quantum elements of the gravitational field. If this means to quantize General Relativity, the general-relativistic identification of the gravitational field with the space time metric has to be taken into account. The quantization must be reasonably sufficient, which implies specifically that the subsequent quantum hypothesis must be foundation free. This can't be accomplished by methods for quantum field hypothetical techniques. One of the fundamental prerequisites for such a quantization technique is, that the subsequent quantum hypothesis has a traditional breaking point that is (in any event roughly, and up to the known phenomenology) indistinguishable from General Relativity. Be that as it may, should gravity not be an essential, yet an incited, lingering, developing connection, it could in all likelihood be an inherently old style marvel. Should Quantum Mechanics be regardless generally substantial, we needed to expect a quantum substrate from which gravity would result as a new traditional marvel. What's more, there would be no contention with the contentions against semi-old style hypotheses, in light of the fact that there would be no gravity at all on the substrate level. The gravitational field would not have any quantum properties to be caught by a hypothesis of Quantum Gravity, and a quantization of General Relativity would not prompt any principal hypothesis. The target of a hypothesis of 'Quantum Gravity' would rather be the ID of the quantum substrate from which gravity results. The requirement that the substrate theory has General Relativity as a classical limit – that it reproduces at least the known phenomenology – would remain. The paper tries to give an overview over the main options for theory construction in the field of Quantum Gravity. Because of the still unclear status of gravity and space time, it pleads for the necessity of a plurality of conceptually different approaches to Quantum Gravity. The most essential motivations for the development of a theory of Quantum Gravity are generally supposed to be based on two (probably interrelated) types of problems(i) the mutual conceptual incompatibility between General Relativity on the one hand and Quantum Mechanics and Quantum Field Theory on the other hand.
This paper takes a look at the two cornerstones of modern physics--Quantum Mechanics and The Theory of Relativity (Both Special and General). The differences and similarities for the two subjects are presented. More of their differences and similarities will emerge with new developments in physics. One can't rule out the possibility of the two being unified into one one fine day. That will herald another triumphant moment in physics. Introduction In 1905, Albert Einstein at the age of twenty-six formulated single-handedly, among others, the Theory of Special Relativity together with his other seminal papers on photoelectricity, Brownian motions of atoms and molecular dimensions. The year has been universally declared the Miraculous Year [1]. Ten years later, he came up with the theory of General Relativity--a new and revolutionary framework on gravity. Meanwhile in Europe a group of young physicists played pivotal role in the birth of Quantum Mechanics. Many of them went on to win Nobel prizes for their monumental contributions. Einstein also won the coveted prize not for Relativity but ironically for Photoelectric Effect. Irony has been part of physics in its history. Relativity with its weird 'Twin Paradox', constancy of the speed of light and the interchangebility between mass and energy (E=[mc.sup.2]) enthralls the public and scientists alike. It provides a way to measure particle masses [2]. The Quantum Theory has its fair share of weirdness and bewilderment. Both Quantum Mechanics and the Theory of Relativity bring forth new ideas in human thoughts. They are among Joanne Baker's 50 physics ideas [3]. Quantum Mechanics and the Theory of Relativity The quantum world where counterintuition reigns supreme is couched in uncertainty as epitomised by Heisenberg's uncertainty principle. Things do not behave in a deterministic way as enshrined and expected in classical Newtonian physics. The microscopic world of the electrons was dictated by randomness and indeterminacy. Albert Einstein was appalled by such dictates that he famously declared: 'God does not play dice with the universe.' The famous Danish physicist Neils Bohr sprang to his feet by saying: 'Stop telling God what to do with his dice.' The sparring between the two stalwarts in physics is legendary. According to Trefil [4], there are a couple of things that need to be said about the uncertainty principle: it does not imply that we cannot know either the position or the velocity of a particle, and it does not require the presence of a conscious mind. Marcus Chown [5] wraps up by saying 'The bitter irony, not lost on Einstein, was that he was the one who, by postulating the existence of the photon, had inadvertently set loose the genie of randomness of physics. The two theories of relativity by Einstein are not couched in randomness however. According to Smoot [6], both implied a radically new cosmology. Many people are of the opinion that with Einstein's theory of relativity, old classical physics is no more in vogue. According to Angier [7], Albert Einstein did not prove that Isaac Newton was wrong. Instead, he showed that Newton's theories of motion and gravity were incomplete, and that new equations were needed to explain the behavior of objects under extreme circumstances, such as when tiny particles travel at or near the speed of light. …
This article is a continuation of Part(I) to demonstrate more aspects for a successful merge of classical mechanics to the quantum theory. The article starts first with the deduction of the general form of the complimentary energy, next a robust firm mathematical proof is given indicates that the complimentary energy has a wave nature and it is a potential energy, then the radiation condition has been determined, a vector formula expresses the corresponding force was deduced and this force was called adhesion force. A mathematical convergence process has proved the duality of the electromagnetic wave parameters and particle parameters, which results in the existence of a “wave-particle” object. While finding the relationship between the electromagnetic wave parameters and particle parameters, a mathematical relationship was found indicating that not every moving charged mass generates a magnetic field. This relationship for the mass was linked to the effective mass tensor, The geometric representation of the constant energy surface and its relationship to the energy levels of both the orbital model (Bohr model) and the cloud model for different geometric 3D shapes were investigated as a sample of the possible geometric interpretations of the energy equation, that is by employing the triangle method, it is possible to create a geometric representation of the constant energy surfaces. The relation between the energy levels, quantum numbers, and band width is represented geometrically. As a result of proving the relationship between the motion of an electromagnetic wave and the motion of a particle associated with the wave, two new, unprecedented mathematical formulas were developed. The first formula specifies a moving charged mass and its relationship to the resulting wavelength. Thus, the radius of the charged mass is obtained in terms of its wavelength and mass density. The second formula specifies the kinetic energy of a photon. The grand potentials are the potential energy of the Newton’s Law of Universal Gravitation, Coulomb’s Law, and Inverse Square Law of Electromagnetic Waves Intensity. From the potential energy of Newton’s law of universal gravitation, the wavelength of the gravitational wave, as well as the wavelength of quantum gravity were deduced. A mathematical relationship was then deduced that determines the lengths of the functions of conic sections, and in particular the length of perimeter of ellipses. From the potential energy of Coulomb’s law of attraction, a mathematical formulation of the energy levels in general for any atom of an element was obtained. This mathematical formulation was compared with the results obtained by Bohr and Schrödinger for the hydrogen atom. As for the inverse square law of electromagnetic radiation intensity, several innovative mathematical equations have been deduced that link different parameters together. Following the contents of this article requires to be quite familiar with the contents of the first part with the same title, as well as a complete understanding of the concepts of intermediate parameters derived and used in the various equations. Otherwise, it will be extremely difficult to follow the contents of this article.
1.General mathematical theory.---Modifications are given in the general derivation of the Langevin-Debye formula by means of quantum mechanics published in part I which are required by the moment now being magnetic rather than electric. The main additions are the appearance of a diamagnetic term, and allowance for the fact that the magnetic moment consists of two parts arising respectively from orbital electronic motions and from the electrons' internal spins. These parts cannot always be treated as rigidly coupled to form a "permanent" resultant moment. The Hamiltonian function used for the internal spin is that of a spherical top.2.Diamagnetism.---The writer's previous claim that Pauli's formula for the diamagnetic susceptibility can be applied to molecules as well as atoms is shown to be invalid because of the anomalous fact that the square of the angular momentum, unlike the average angular momentum, does not vanish even in SSS states when there is more than one nucleus. Pauli's formula is instead an upper limit to the diamagnetism in non-monatomic molecules and is a good approximation when the Schr\"odinger wave function has nearly as much symmetry as in an atomic SSS state.3.Paramagnetism of atoms.---Limiting values for the paramagnetic susceptibilities of atoms are $\ensuremath{\chi}=N\frac{[4s(s+1)+k(k+1)]{\ensuremath{\beta}}^{2}}{3kT}$ and $\ensuremath{\chi}=[\frac{N{g}^{2}j(j+1){\ensuremath{\beta}}^{2}}{3kT}]+N\ensuremath{\alpha}$ where $\ensuremath{\beta}$ is the Bohr magneton and $\ensuremath{\alpha}$ is a constant. These two formulas are rigorously applicable when the multiplet intervals are respectively very small or very large compared to kT\mathrm{kT}kT, and are valid regardless of whether the magnetic field is strong enough to change the quantization by producing a Paschen-Back effect. The formula for small multiplets yields susceptibilities slightly different from those given by Laporte and Sommerfeld's expression for this case, and is much simpler, as they overlooked the contribution of the portion of the magnetic moment which is perpendicular to the invariable axis.4.Paramagnetism of molecules.---The susceptibility is calculated on the basis of the Hund theory of molecular quantization. Formulas are given applicable to his couplings of type (a) and type (b) provided in the former the multiplet intervals are either very large or very small compared to kT\mathrm{kT}kT. The experimental susceptibilities for O2{\mathrm{O}}_{2}O2​ and ClO2{\mathrm{O}}_{2}O2​ are in accord with the assumption that the normal states are respectively 3S^{3}S3S and 2S^{2}S2S terms. In the particular case of SSS terms the numerical results are the same in the atomic and molecular formulas, but, unlike previous theories, it is not necessary to suppose the orbits are as freely oriented in molecules as in atoms. Polyatomic molecules may have lower paramagnetic susceptibilities than diatomic ones because the dissymmetry causes large fluctuations in electronic angular momentum.5.Paramagnetism of nitic oxide.---Spectroscopists have recently found that the normal states of the NO molecule are 2P^{2}P2P terms separated by 120.9 ${\mathrm{cm}}^{\ensuremath{-}1}$. This permits an unambigous calculation of the susceptibility of NO which agrees with the experimental value within 1.5 per cent. Deviations from Curie's law are calculated which result from the doublet interval being comparable with kT\mathrm{kT}kT. These deviations should be detectable experimentally if the susceptibility of NO could be measured over a wide temperature range.
In the early 20th century, Planck, Einstein, Bohr, Sommerfeld, and de Broglie became the pioneers of quantum physics. Because the Schrödinger equation used the wrong energy relationship, it misled people’s understanding of quantum theory. Newtonian mechanics and Leibniz dynamics are correct. But Newton’s first law was tampered with by the British mathematician Mott during his translation, which excluded uniform circular motion from inertia; Leibniz’s kinetic energy mυ2 was modified by French engineer Coriolis to an engineering approximation of mυ2/2. Hamilton mistakenly applied the approximate kinetic energy formula of Coriolis in engineering mechanics to the dynamic analysis in theoretical physics, and established an incorrect Hamiltonian energy equation. Schrödinger ignored Sommerfeld’s research on the constant velocity of electrons in atoms, υ = αc, and thus the constant momentum and constant kinetic energy of electrons. He expressed the constant kinetic energy term of electrons as an operator that hides the velocity variable, and established the wave equation based on the incorrect Hamiltonian energy relationship. The Schrödinger equation deals with the ground state of hydrogen atoms, where electrons die when they reach twice the Bohr radius, which contradicts the stable existence of atoms. The Schrödinger ‎equation has been around for almost a century, and the quantum physics of the new millennium ‎should be a new quantum physics without the Schrödinger equation.