In the conventional theory of the ground state of heliu m ato m, any solution of the two-electron Schrodinger equation is wrong! That is caused by a strong imbalance of proportions of the attraction versus repulsion operators' acting on a wave function, in the initial differential Schrodinger equation and in its integral algebraic form. In the differential equation, the attraction operators act on the radial part of wave function independently fro m one another obeying the true proportion: one attraction versus one repulsion per electron. But the resulting wave function turns out to satisfy the wrong integral proportion: two attraction energies versus one repulsion energy per electron. The underlying contradiction is un-coincidence of the additivity rules of energies and energy operators: whereas energies of the electrons may be summed the corresponding energy operators referred to different electrons may not. Consequences of this principal contradiction are d iscussed.
In the conventional theory of the ground state of heliu m ato m, any solution of the two-electron Schrodinger equation is wrong! That is caused by a strong imbalance of proportions of the attraction versus repulsion operators' acting on a wave function, in the initial differential Schrodinger equation and in its integral algebraic form. In the differential equation, the attraction operators act on the radial part of wave function independently fro m one another obeying the true proportion: one attraction versus one repulsion per electron. But the resulting wave function turns out to satisfy the wrong integral proportion: two attraction energies versus one repulsion energy per electron. The underlying contradiction is un-coincidence of the additivity rules of energies and energy operators: whereas energies of the electrons may be summed the corresponding energy operators referred to different electrons may not. Consequences of this principal contradiction are d iscussed.
The Schrodinger equation has been considered to be a postulate of quantum physics, but it is also perceived and derived heuristically as the quantum equivalent of the classical energy relation. We indicate that the Schrodinger equation cannot be a physical postulate, and we show that the heuristic derivations wrongly consider that the particle kinetic energy is proportional to the square of the momentum operator acting on the wavefunction. The correct term is proportional to the square of the momentum. Analyzing particle interactions, we realize that particles have multiple virtual motions and that each motion is accompanied by a wave that has constant amplitude. Accordingly, we define the wavefunction as the superposition of the virtual waves of the particle. As a result, quantum mechanics becomes a local and global theory, while in the traditional formulation it is a local theory. In several interaction settings we can tell what particle motions arise and explain the outcomes in simple and tangible terms. Most importantly, the mathematical foundation of quantum mechanics becomes clear and justified, and we derive the Schrodinger, Dirac, etc. equations as the conditions the wavefunction must satisfy at each space-time point in order to fulfill the respective total energy equation.
The Schrodinger equation is an equation that describes the properties of a wave. The Schrodinger equation is solved using a variable separation method that produces a wave function. The wave function using the variable separation method is divided into 2 parts, namely the radial part and the angular part. The energy spectrum states the energy levels of electrons. Energy spectrum and wave function are related to each other. The energy level in the Schrodinger wave function in the form of kinetic energy is the energy for electrons to move from one point to another. The research aims to describe the kinetic energy spectrum of electrons in the radial wave function. The type of research used is basic research, namely the development of existing theories. The result obtained is a radial wave function with a certain quantum number n and an integrated Laplace constant that can produce electron kinetic energy, namely by integrating the wave function with each quantum number. The kinetic energy has its own value according to the quantum number. Kinetic energy in quantum numbers (n = 1,l = 0, Ek =171.18 eV ; n =2,l = 0, Ek =399.09 eV n =2,l = 1, Ek =152.16 eV n =3,l = 0, Ek =5096.81 eV n =3,l = 1, Ek =81142.43 eV n =3,l = 2, Ek =21.979 eV). The conclusion of this research is that the kinetic energy spectrum of electrons produces a directly proportional relationship to the quantum number n, where the greater the quantum number n, the greater the spectrum or kinetic energy level of the electron.
The Bohr formulation—the original one—is now largely a matter of history. The usual career of a theory was its fate. It explained much, but it failed at the first signs of complication, even for the simplest molecules as hydrogen and helium. Some results were either only approximate in a loose or incomplete fashion, e.g. in the application of the correspondence principle to intensities, the only reliable predictions being only for an absence of certain lines, or they quite disagreed with experiment, e.g. in the case of the hydrogen molecule and the hydrogen molecule ion, the normal and excited states of helium, the anomalous Zeeman effect, the Ramsauer effect (the phenomenon of the deflection of electrons at low speeds being less than at higher speeds in atomic collisions), and in the treatment of problems where more than one electron was involved. In the last mentioned cases the perturbation method, so successful in solving “many-body” problems in celestial mechanics, failed completely because systems of several electrons, possessing frequencies of the order of light waves, cannot interact classically. A bit of much forced pragmatism was practiced in treating the many electron atom as a variation of the hydrogen atom. Besides, there were technical oddities, like ½ quantum numbers, and impenetrated anologies between visible and X-ray spectra.
A many-boson model is formulated and expressions for its exact eigenstates and energies are obtained for both an arbitrary finite and an infinite number of bosons. The Hamiltonian of the model contains interactions between bosons whose momenta have equal magnitudes but opposite directions. The matrix elements of this interaction are taken to be a constant over a range of momenta surrounding k = 0. The ground state of the 2N-particle system is shown to be a product of N pair-creation operators acting on the vacuum state. Each of these pair-creation operators depends upon one of N parameters which are called pair energies. The N pair energies are shown to satisfy a coupled system of nonlinear algebraic equations. The energy of the state is the sum of the pair energies and the occupation probabilities of the single-particle levels are given as simple functions of the pair energies. Similar results are derived for the excited states of the system and for the states of an odd number of particles. These results are valid for both a repulsive and an attractive interaction, since they only depend upon the form of the interaction. The equations are solved algebraically for two model systems. The first of these is one whose single-particle kinetic energy takes on only one value. The equations for this system are solved for an arbitrary interaction strength and it is shown that the pair energies are proportional to the zeros of certain Laguerre polynomials. The second system is one in which the single-particle kinetic energy can take on two values. The equations for this system are solved in the strong repulsive-interaction limit and it is shown that the pair energies are proportional to the zeros of certain Jacobi polynomials. The excitation energies of this second system are shown to be proportional to 1/n and the occupations of the two single-particle levels in the ground state are shown to be proportional to n, where n is the total number of particles. For a repulsive interaction and an arbitrary single-particle spectrum, the algebraic equations for the pair energies are converted into an approximate integral equation for the density of roots which is accurate to order 1/n. This integral equation is solved for a strong interaction which, in the context of this model, means an interaction whose strength is greater than a constant times 1/V⅔ in the limit of a large volume. From this solution, the following results are obtained: (1) the lowest two single-particle levels have occupations of order n; (2) the excitation spectrum is that of a set of noninteracting quasiparticles; and (3) the quasiparticle spectrum has two zeros corresponding to the lowest two single-particle levels. Apart from the presence of two zeros, the quasiparticle spectrum does not differ significantly from that of the noninteracting particles.
The “quantum” world, within the framework of which “outstanding” scientific discoveries are being made now, is built on initially laid nonsense. Quantum theory was initially built on incorrect adjustment by Schrödinger of two-dimensional “solutions” of the One-dimensional harmonic oscillator equation. These are the consequences of this fitting and “excited minds.” This is the reason why quantum mechanics is not necessary to UNDERSTAND, but it is necessary to ACCEPT. But they accepted and canonized, as is shown in this work, non-physical, rough, approximate solutions. And it is on the basis of these solutions that electron orbitals, widely used in fundamental and applied science, are constructed. So the “Terrible Secret” of the theorists is that in fact without having a basic model they are exclusively engaged in fitting Schrödinger’ssolutions.