The existing methods for calculating the energy of stationary states relate it to the energy of the electron, considering it negative in the atom. Formally, choosing a point that corresponds to zero potential energy you can assign a negative value to the electron energy. However, this approach does not answer many other questions, for example, the actual value of the energy of stationary states is unknown, but only the difference in energies between stationary states is known; the concept of “minimum energy of the system” loses its meaning (choosing the origin of the energy reference, we replace the minimum with the maximum, or vice versa); the physical reason for the stability of stationary states is not clear; it is impossible to reveal the physical reason for the introduction of selection rules, since the Heisenberg uncertainty relations exclude the analysis of the transition mechanism, replacing it with the concept of a “quantum leap”. Let us show that the energy of stationary states is the energy of a spherical capacitor, the covers of which are spheres whose radii are equal to the radius of the nuclear and corresponding stationary state. The energy of the ground state in the hydrogen atom is 0.8563997 MeV. The presence of charges and a magnetic field presupposes the circulation of energy in the volume of the atom (the Poynting vector is not zero). Revealed quantization of the angular momentum of the electromagnetic field in stationary states is [Formula: see text]. The change in the angular momentum of the electromagnetic field during transitions between stationary states in atoms removes the physical grounds for introducing selection rules. The analysis shows that the Heisenberg uncertainty relations are not universal, and their application in each specific case must be justified.
The existing methods for calculating the energy of stationary states relate it to the energy of the electron, considering it negative in the atom. Formally, choosing a point that corresponds to zero potential energy you can assign a negative value to the electron energy. However, this approach does not answer many other questions, for example, the actual value of the energy of stationary states is unknown, but only the difference in energies between stationary states is known; the concept of “minimum energy of the system” loses its meaning (choosing the origin of the energy reference, we replace the minimum with the maximum, or vice versa); the physical reason for the stability of stationary states is not clear; it is impossible to reveal the physical reason for the introduction of selection rules, since the Heisenberg uncertainty relations exclude the analysis of the transition mechanism, replacing it with the concept of a “quantum leap”. Let us show that the energy of stationary states is the energy of a spherical capacitor, the covers of which are spheres whose radii are equal to the radius of the nuclear and corresponding stationary state. The energy of the ground state in the hydrogen atom is 0.8563997 MeV. The presence of charges and a magnetic field presupposes the circulation of energy in the volume of the atom (the Poynting vector is not zero). Revealed quantization of the angular momentum of the electromagnetic field in stationary states is [Formula: see text]. The change in the angular momentum of the electromagnetic field during transitions between stationary states in atoms removes the physical grounds for introducing selection rules. The analysis shows that the Heisenberg uncertainty relations are not universal, and their application in each specific case must be justified.
This paper proposes a fundamentally new approach to the study of stationary states in atoms, which is based on the analysis of the energy of electric and magnetic fields. The circulation of the electromagnetic field in the stationary states of the atom was discovered and the mechanism of optical transitions due to the continuous change of the circulating energy was clarified. The difference between circulating energy flows in the initial and final states is emitted (or absorbed) in the form of a quantum of light. A universal relation for determining the lifetime of excited states is proposed.
The energy structures and transition energies of single-electron atoms and ions are presented. Five Nobel Prizes in Physics were awarded for the theories discussed in this chapter. We first review the Bohr model, which was based on quantized angular momentum and classical circular orbits. The wave model of Schrödinger followed, in which spherical boundary conditions quantized polar and azimuthal standing waves. The energies were identical to Bohr’s, but transition selection rules dictated the change in angular momentum of the system during absorption and emission. Dirac incorporated electron spin and relativistic energies, resulting in energy shifts and fine structure splitting of the energy levels for non-zero angular momentum states. Feynman and Swinger incorporated quantization of the electric vector potential. This physics broke energy degeneracies in the Dirac model and correctly predicted the famous Lamb shift. In this chapter, each of these models are described in detail. The final full characterization of the energy levels and transitions are presented. The chapter ends with a discussion on isotope shifting and transitions to the continuum (ionization/recombination).
A rigorous derivation of the Schrödinger theory from the Pauli (or Dirac) theory implies that the Schrödinger equation describes an electron in an eigenstate of spin. Furthermore, the ground-state kinetic energy is completely determined by the electron spin density. This can be explained by interpreting the spin as an orbital angular momentum, which is necessarily accompanied by a kinetic energy. Thus, the spin is a zero-point angular momentum associated with the zero-point energy of the electron. Since the dispersion in electron momentum is determined by the zero-point energy, the Heisenberg uncertainty relations for an electron can be interpreted as a property of the electronspin motion. The kinetic interpretation of spin and the statistical interpretation of quantum mechanics can be jointly sustained by regarding the electron as a point particle. It follows that stationary electron states are sources of fluctuating electric fields. There is reason to believe that these fluctuating fields are responsible for the Van der Waals force and can be identified with electromagnetic vacuum field fluctuations. The kinetic interpretation of spin then implies that the Van der Waals forces are spin dependent. These ideas are not only consistent with the conventional mathematical formalism of quantum mechanics, they provide a more complete and coherent interpretation of many details in the formalism than does the alternative Copenhagen interpretation. They present some difficulties, however, which, if the kinetic interpretation of spin is correct, probably require some modification of quantum electrodynamics to be resolved.
In many practical cases a stationary system is perturbed in some way, inducing it to undergo transitions between the otherwise stationary states. Perhaps the best example concerns the radiative transitions of atomic electrons in which the disturbance of an external electromagnetic field causes the electrons to jump between energy levels, emitting or absorbing photons. Equation is a statement of the classical law of conservation of energy. The stimulated emission and absorption of radiation both have close classical analogues. If a simple harmonic oscillator is driven by a sinusoidal electromagnetic field it can gain or lose energy depending on phase angles. The existence of spontaneous emission implies that all excited states of electrical systems are unstable and will eventually decay to the ground state by photon emission. Quantum systems thus comply with the fundamental principle that physical systems tend to seek out their state of lowest energy and maximum entropy.
The "quantum equation" should "carry the quantum conditions in itself" (Second Commun., p. 511); 2. There should be a special mathematical method for solving the stationary Schrödinger equation, which accounts for the non-classical character of the quantization problem, ie, which is different from the classical eigenvalue methods for calculating the (eigen)modes of strings, resonators and so on (ibid., p. 513);3. The derivation should uniquely decide, that the energy rather than the frequency values are discretized (ibid., pp.511, 519), since only the former means true quantization, while the latter corresponds to the classical discretization mentioned in requirement 2;4. The use of the classical expressions for the kinetic and potential energies should be justified (Fourth Commun., p. 113).Schrödinger's requirements 1 and 2 mean, that -contrary to the very title of the papersquantization is actually not an eigenvalue problem.For in the latter the discretization is imposed not by the differential equation itself, but by the boundary conditions, and this is the classical discretization for standing waves in organ pipes etc.I will fulfill all four requirements by treating quantization as a selection problem.The number of stationary states of a quantum system is smaller than that of a classical system [6].I will describe, (i), the selection of quantum systems out of the set of all mechanical systems and, (ii), the selection of their stationary states out of the continuum of classical stationary states.Earlier arguing [19][10] is improved and extended in several essential points. Elements of an Eulerian representation of classical mechanics Euler's axiomsLeonhard Euler [20][21][22][23][24][25] was the first to apply the calculus to all areas of mathematics and mechanics of his time, and he developed novel methods, such as the calculus of variations and topology.Moreover, he worked out an axiomatic of mechanics, where only Newton's Law (axiom) 1 concerning the conservation of stationary states is retained as an axiom, while Newton's Laws (axioms) 2 and 3 concerning the change of stationary states are treated as problems to be solved (for a detailed account, see [19][10][45]).This allows for introducing alternative equations of motion without loosing the contact to CM.The existence of stationary states is postulated in the following axioms (as in Newton's axioms, rotatory motion is not considered). Axiom E0: Every body is either resting or moving.This means, that the subsequent axioms E1 and E2 are not independent of each other; they exclude each other and, at once, they are in harmony with each other [22].
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.