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Register a new userThe Nature of Schrodinger Equation -- On Quantum Physics Part I
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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 particles 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 classical world and quantum world.
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It was recently advanced the argument that Unruh effect emerges from the study of quantum field theory in quantum space-time. Quantum space-time is identified with the Hilbert space of a new kind of quantum fields, the accelerated fields, which are defined in momentum space. In this work, we argue that the interactions between such fields offer a clear distinction between flat and curved space-times. Free accelerated fields are associated with flat spacetime, while interacting accelerated fields with curved spacetimes. Our intuition that quantum gravity arises via field interactions is verified by invoking quantum statistics. Studying the Unruh-like effect of accelerated fields, we show that any massive object behaves as a black body at temperature which is inversely proportional to its mass, radiating space-time quanta. With a heuristic argument, it is shown that Hawking radiation naturally arises in a theory in which space-time is quantized. Finally, in terms of thermodynamics, gravity can be identified with an entropic force guaranteed by the second law of thermodynamics.
A covariant non-local extention if the stationary Schrodinger equation is presented and its solution in terms of Heisenbergss matrix quantum mechanics is proposed. For the special case of the Riesz fractional derivative, the calculation of corresponding matrix elements for the non-local kinetic energy term is performed fully analytically in the harmonic oscillator basis and leads to a new interpretation of non local operators in terms of generalized Glauber states. As a first application, for the fractional harmonic oscillator the potential energy matrix elements are calculated and the and the corresponding Schrodinger equation is diagonalized. For the special case of invariance of the non-local wave equation under Fourier-transforms a new symmetry is deduced, which may be interpreted as an extension of the standard parity-symmetry.
By constructing the commutative operators chain, we derive the integrable conditions for solving the eigenfunctions of Dirac equation and Schrodinger equation. These commutative relations correspond to the intrinsic symmetry of the physical system, which are equivalent to the original partial differential equation can be solved by separation of variables. Detailed calculation shows that, only a few cases can be completely solved by separation of variables. In general cases, we have to solve the Dirac equation and Schrodinger equation by effective perturbation or approximation methods, especially in the cases including nonlinear potential or self interactive potentials.
In this paper we prove the following: (1) The basic error of time-dependent perturbation theory is using the sum of first finite order of perturbed solutions to substitute the exact solution in the divergent interval of the series for calculating the transition probability. In addition quantum mechanics neglects the influence of the normality condition in the continuous case. In both cases Fermi golden rule is not a mathematically reasonable deductive inference from the Schrodinger equation. (2) The transition probability per unit time deduced from the exact solution of the Schrodinger equation is zero, which cannot be used to describe the transition processes.
Irrotational ow of a spherical thin liquid layer surrounding a rigid core is described using the defocusing nonlinear Schrodinger equation. Accordingly, azimuthal moving nonlinear waves are modeled by periodic dark solitons expressed by elliptic functions. In the quantum regime the algebraic Bethe ansatz is used in order to capture the energy levels of such motions, which we expect to be relevant for the dynamics of the nuclear clusters in deformed heavy nuclei surface modeled by quantum liquid drops. In order to validate the model we match our theoretical energy spectra with experimental results on energy, angular momentum and parity for alpha particle clustering nuclei.
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