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.
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.
Abstract Steven Weinberg, one of the founders of the Standard Model of Physics, asked years ago [1]: is the wave function of quantum mechanics real, or is it just used by scientists to calculate? We try to find the answer. We study the general solution of the Schrödinger equation mathematically. We will prove that for satisfying the Schrödinger equation, the particle should possess a helical structure of mass density. Then we will prove further that (i) charged elementary particles and atomic nucleus fall into two categories: they have charge or, but different directions of charges helices, like right-handed electron and left-handed electron etc. (ii) Charge (or) distributes double helically on the particle side boundary. It generates and carries a double helix external electric field with the same velocity. (iii) This E-wave will be proved is just the de Broglie wave. (iv) Its function is particle’s state function in quantum mechanics. (v) Charged particle itself and the de Broglie E-wave it carries form a particle-wave hybrid structure. The E -wave exhibits all the possible states and probabilities; as for the particle itself it can take only one basis state randomly, such as at an eigen state in the atom and molecular or at a point on the interference pattern. (vi) The orbital motion of an electron in the lower energy layers of atom and molecule does not radiate EM energy to collapse into the nucleus. (vii) Self-interference of the hybrid structure can better explain the single particle double-slit 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.
Till 1925 the idea of what the quantum theory would be was unknown. During 1925 three different but equivalent versions of quantum theory were proposed – Schrödinger-proposed wave mechanics; Heisenberg-developed matrix mechanics and Dirac-introduced operator theory. Considering the de Broglie’s matter waves Erwin Schrödinger, an Austrian physicist, argued that if a particle like an electron behaves as a wave then the equation of wave motion could be successfully applied to it. He postulated a function varying in both space and time in a wave-like manner (hence called wave function and denoted it as ψ). This function is generally complex and assumed to contain information about a system. Schrödinger set up a linear and time-dependent wave-like equation, called Schrödinger wave equation, to describe the wave aspect of a particle taking account of de Broglie’s relation for wavelength. Physically, |ψ(X, t)|2, where ψ(X, t) is the solution of the Schrödinger equation, is interpreted as position probability density. That is, |ψ(X, t)|2 is the probability density of observing a particle at position X at time t. ψ does not give exact outcomes of observations but helps us to know all possible events and their probabilities . Further, the probability interpretation allows us to find the average or expected result of a set of measurements on a quantum system.
The Schrödinger equation was really postulated rather than derived. But we can see why it was postulated. It has been proven to be valid, in that it provides information about small, slow moving particles subject to a wide variety of potentials. The derivation of the time-dependent Schrödinger equation (TDSE) follows rather directly from assuming a free particle wave: Ψ = e i(kx-ωt) . If this wave function is plugged into the classical wave equation, and quantum principles are used, the two sides of the equation are not equal (this means this function does not "solve" the equation). The quantum principles required are an understanding of the photoelectric effect (by which E = ħω) and the de Broglie hypothesis (λ = h/p). Using these relationships, we show that one derivative of time is equal to a double derivative with respect to position, with a few proportionality factors mixed in. Thus, the TDSE for a free particle is just a statement that kinetic energy equals total energy . For a non-free particle (subject to a potential), potential must merely be added to the left-hand side of the equation, to yield kinetic energy plus potential energy equals total energy .
We investigate the meaning of the wave function by analyzing the mass and charge density distributions of a quantum system. According to protective measurement, a charged quantum system has effective mass and charge density distributing in space, proportional to the square of the absolute value of its wave function. In a realistic interpretation, the wave function of a quantum system can be taken as a description of either a physical field or the ergodic motion of a particle. The essential difference between a field and the ergodic motion of a particle lies in the property of simultaneity; a field exists throughout space simultaneously, whereas the ergodic motion of a particle exists throughout space in a time‐divided way. If the wave function is a physical field, then the mass and charge density will be distributed in space simultaneously for a charged quantum system, and thus there will exist gravitational and electrostatic self‐interactions of its wave function. This not only violates the superposition principle of quantum mechanics but also contradicts experimental observations. Thus the wave function cannot be a description of a physical field but be a description of the ergodic motion of a particle. For the later there is only a localized particle with mass and charge at every instant, and thus there will not exist any self‐interaction for the wave function. It is further argued that the classical ergodic models, which assume continuous motion of particles, cannot be consistent with quantum mechanics. Based on the negative result, we suggest that the wave function is a description of the quantum motion of particles, which is random and discontinuous in nature. On this interpretation, the square of the absolute value of the wave function not only gives the probability of the particle being found in certain locations, but also gives the probability of the particle being there. The suggested new interpretation of the wave function provides a natural realistic alternative to the orthodox interpretation, and it also implies that the de Broglie‐Bohm theory and many‐worlds interpretation are wrong and the dynamical collapse theories are in the right direction by admitting wavefunction collapse.
We propose that the Schrodinger equation results from applying the classical wave equation to describe the physical system in which subatomic particles play random motion, thereby leading to quantum mechanics. The physical reality described by the wave function is subatomic particle moving randomly. Therefore, the characteristics of quantum mechanics have a dual nature, one of them is the deterministic nature carried on from classical physics, and the other is the probabilistic nature coined by particle's random motion. Based on this model, almost all of open questions in quantum mechanics can be explained consistently, which include the particle-wave duality, the principle of quantum superposition, the interference pattern of double-slit experiments, and the boundary between the classical world and the quantum world. The current quantum mechanics is a mixture of matrix mechanics and wave mechanics, which are sharply conflicting in principle. Matrix mechanics treats quantum particles as classical particles with fixed relation between the particle's position and its momentum. The matrix mechanics, in fact, belongs to the old quantum theory. Both Born's non-commutative relation and Heisenberg uncertainty relation originate from matrix mechanics. However, in wave mechanics, there is no any fixed relation between the particle's position and its momentum, and the particle's position and its momentum belong to immeasurable physical quantities. Therefore, there is no need for non-commutative relation and uncertainty relation in wave mechanics.