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Advanced Studies in Theoretical Physics

Why atomic and subatomic particles have wave property and satisfy the Schrodinger Equation? It infers the structures of these ± charged particles

Sennian Chen

Published Jan 1, 2021• 2 citations
Publisher
DOI
10.12988/astp.2021.91522

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If We Postulate Atomic and ± Subatomic Particles are Size Particles and Satisfy the Schrodinger Equation, what will be the Inferences?

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In quantum mechanics, atomic and subatomic particles are treated as waves. The idea of wave function and wave function collapse brought us great success but left us different opinions. Is there a way it can avoid the different opinions and give us more? We try to postulate directly that these particles are size particles and satisfy the Schrodinger equation. Start from the general solution of free particle’s Schrodinger equation, we will prove: (i) To satisfy the Schrodinger equation, the size particle must possess a circular polarized structure of the plane vector（a complex number）like the electric vector E in the circular polarized light; its modular is mass density. (ii) These particles fall into two categories: they have the same sign of negative charge e or positive charge e, but different directions of mass density and charged helices, like left handed electron and right handed electron etc. (iii) The spin of the particle has its mechanism, it is formed by the motion of the helices structure of mass plus intrinsic self rotation. (iv) Negative charge e (or positive charge e) distributes double helically on the particle side boundary. It produces and carries a circular polarized electric field E with the same velocity of the particle. It forms a circular polarized E-wave. This wave will be proved is just the de Broglie wave and the E-wave function is just the particle’s state function in quantum mechanics. Such charged particle is consisted of the particle itself and the de Broglie wave; they form a particle-wave hybrid structure. The E- wave exhibits all possible states with possibility in the atom, molecule or interference pattern; as for the particle itself, it cannot split into two or move with two velocity at the same time. It can only locate at one basic state any moment, such as in an eigen state of the atom or at a point in the interference pattern. It is the self-interference of the hybrid structure of the particle makes the one after one single particle form double-slits interference.

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Until now, we do not know whether elementary particles have structure, but we cannot assert that elementary particles do not have structure, because all experiences tell us that the properties of non-living and living things are closely related to their structure. As their foundation, can the microscopic particles be excluded? Do photons and charged fermions have structure? What structure? We study the key to the Schrödinger computation that accurately reproduce the energy levels of the Bohr model and the general solution of Schrödinger equation mathematically; we found to satisfy Schrödinger equation the charged fermions must possess a double helix structure of mass density. Such structures plus partial self-rotation make them quantized and a fixed value spin or . We prove that the Maxwell wave equation is simultaneously the Klein-Gordon equation for electromagnetic waves. Then we prove that photons have a double helix structure of EH-energy that makes photons quantized and a fixed value spin or . There is a charge in the electron (and charged fermions); a pair of charges in the photons, they distribute double helically along their side boundaries; these charges produce and carry a circular polarized E-wave and EH-wave respectively. They form two traveling-wave-particle hybrid structures. It is such hybrid structures give them traveling-wave-particle duality. Such dualities can exhibit their wave property and particle property simultaneously in the same experiments. At last, we prove that the electron cloud photo not only exhibits the probability distribution of electrons but also proves the existence of electrons’ trajectories around the nucleus; the electrons’ motions make the probability distribution. The electron probability distribution around the nucleus is causal. At last we prove that the electron in the main shells (the Eigen states) of a multi-electron atom does not radiate pure EM energy, not fall to the nucleus.

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Photon and charged elementary particles have many commonalities like constant spin, duality, etc. The purpose of this paper is trying to find out why such particles have the commonalities and how to make the commonalities. The first part of this paper is to derive and prove that the photon is consisted of an energy packet and a closely connected circular polarized EM wave with much smaller energy. The energy packet is a thin piece of circular polarized EH field wrapped by a cylindrical side membrane with helical distributed . Double helix structure of field EH in the energy packet plus intrinsic speed c being proved makes almost all the basic properties of photon in the paper. The wave-particle properties in the structure of photon plays a roll together in the process of emission, absorption and interference. Such structure makes the photon to act as both a wave and a particle at the same time, not “exhibit different characters for different phenomenon”. It makes the dispute in the double slit experiment unnecessary. Charged elementary particles produced from a photon in the pair production will be proved in the paper it is split equally point to point from the photon. So the particles possess double helix structure of mass density and charge (or ). The helically distributed charge (or ) carries a circular polarized external E-field to move with the same velocity (a wave really). Of the charged elementary particle and of this E-wave will be proved to satisfy the de Broglie Relation here. It naturally leads to the differential equation of motion of such particles mathematically as same as the Schrodinger equation. Such differential equation of motion for the non-relativistic particles will be proved it is for the circular polarized structure and wave. Difference between helical (or ) and helical makes the charged elementary particles and photon distinguishable or undistinguishable by the magnetic B effect and to obey different statistics, F-D statistics or B-E statistics; and obey the Pauli Exclusion Principle or not. Since the spin direction of the photon and charged elementary particles are decided by the direction of helical structure, anyone of these particles can only possess a definite direction of spin, so the entanglement is like a pair of gloves disregard of how far the distance between them. Because a particle cannot locate at two positions or possess two different magnitudes of energy at the same time, (otherwise, the particle will split or move with different speed simultaneously), the particle itself can take only one basis state (e.g. at a point in the interference pattern or in an eigen state of the atom or molecule) any time. Therefore, the idea like wave function collapse, electron cloud and both alive and dead Schrodinger cat are no longer necessary. At last, it is a proof that there is a particular relativistic property of the charged elementary particles in the equal energy process. It will affect the physical and chemical process in the atom and molecule.

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In quantum mechanics, atomic and subatomic particles are treated as waves. The idea of wave function and wave function collapse brought us great success but left us different opinions. Is there a way it can avoid the different opinions and give us more? We try to postulate directly that these particles are size particles and satisfy the Schrodinger equation. Start from the general solution of free particle’s Schrodinger equation, we will prove: (i) To satisfy the Schrodinger equation, the size particle must possess a circular polarized structure of the plane vector（a complex number）like the electric vector E in the circular polarized light; its modular is mass density. (ii) These particles fall into two categories: they have the same sign of negative charge e or positive charge e, but different directions of mass density and charged helices, like left handed electron and right handed electron etc. (iii) The spin of the particle has its mechanism, it is formed by the motion of the helices structure of mass plus intrinsic self rotation. (iv) Negative charge e (or positive charge e) distributes double helically on the particle side boundary. It produces and carries a circular polarized electric field E with the same velocity of the particle. It forms a circular polarized E-wave. This wave will be proved is just the de Broglie wave and the E-wave function is just the particle’s state function in quantum mechanics. Such charged particle is consisted of the particle itself and the de Broglie wave; they form a particle-wave hybrid structure. The E- wave exhibits all possible states with possibility in the atom, molecule or interference pattern; as for the particle itself, it cannot split into two or move with two velocity at the same time. It can only locate at one basic state any moment, such as in an eigen state of the atom or at a point in the interference pattern. It is the self-interference of the hybrid structure of the particle makes the one after one single particle form double-slits interference.
Until now, we do not know whether elementary particles have structure, but we cannot assert that elementary particles do not have structure, because all experiences tell us that the properties of non-living and living things are closely related to their structure. As their foundation, can the microscopic particles be excluded? Do photons and charged fermions have structure? What structure? We study the key to the Schrödinger computation that accurately reproduce the energy levels of the Bohr model and the general solution of Schrödinger equation mathematically; we found to satisfy Schrödinger equation the charged fermions must possess a double helix structure of mass density. Such structures plus partial self-rotation make them quantized and a fixed value spin or . We prove that the Maxwell wave equation is simultaneously the Klein-Gordon equation for electromagnetic waves. Then we prove that photons have a double helix structure of EH-energy that makes photons quantized and a fixed value spin or . There is a charge in the electron (and charged fermions); a pair of charges in the photons, they distribute double helically along their side boundaries; these charges produce and carry a circular polarized E-wave and EH-wave respectively. They form two traveling-wave-particle hybrid structures. It is such hybrid structures give them traveling-wave-particle duality. Such dualities can exhibit their wave property and particle property simultaneously in the same experiments. At last, we prove that the electron cloud photo not only exhibits the probability distribution of electrons but also proves the existence of electrons’ trajectories around the nucleus; the electrons’ motions make the probability distribution. The electron probability distribution around the nucleus is causal. At last we prove that the electron in the main shells (the Eigen states) of a multi-electron atom does not radiate pure EM energy, not fall to the nucleus.
Photon and charged elementary particles have many commonalities like constant spin, duality, etc. The purpose of this paper is trying to find out why such particles have the commonalities and how to make the commonalities. The first part of this paper is to derive and prove that the photon is consisted of an energy packet and a closely connected circular polarized EM wave with much smaller energy. The energy packet is a thin piece of circular polarized EH field wrapped by a cylindrical side membrane with helical distributed . Double helix structure of field EH in the energy packet plus intrinsic speed c being proved makes almost all the basic properties of photon in the paper. The wave-particle properties in the structure of photon plays a roll together in the process of emission, absorption and interference. Such structure makes the photon to act as both a wave and a particle at the same time, not “exhibit different characters for different phenomenon”. It makes the dispute in the double slit experiment unnecessary. Charged elementary particles produced from a photon in the pair production will be proved in the paper it is split equally point to point from the photon. So the particles possess double helix structure of mass density and charge (or ). The helically distributed charge (or ) carries a circular polarized external E-field to move with the same velocity (a wave really). Of the charged elementary particle and of this E-wave will be proved to satisfy the de Broglie Relation here. It naturally leads to the differential equation of motion of such particles mathematically as same as the Schrodinger equation. Such differential equation of motion for the non-relativistic particles will be proved it is for the circular polarized structure and wave. Difference between helical (or ) and helical makes the charged elementary particles and photon distinguishable or undistinguishable by the magnetic B effect and to obey different statistics, F-D statistics or B-E statistics; and obey the Pauli Exclusion Principle or not. Since the spin direction of the photon and charged elementary particles are decided by the direction of helical structure, anyone of these particles can only possess a definite direction of spin, so the entanglement is like a pair of gloves disregard of how far the distance between them. Because a particle cannot locate at two positions or possess two different magnitudes of energy at the same time, (otherwise, the particle will split or move with different speed simultaneously), the particle itself can take only one basis state (e.g. at a point in the interference pattern or in an eigen state of the atom or molecule) any time. Therefore, the idea like wave function collapse, electron cloud and both alive and dead Schrodinger cat are no longer necessary. At last, it is a proof that there is a particular relativistic property of the charged elementary particles in the equal energy process. It will affect the physical and chemical process in the atom and molecule.