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新量子論の基本原理

Yoshifumi Ito

Published Dec 24, 2005• 0 citations
OpenAlex

Abstract

In this article, we established the fundamental principles of new quantum theory. At first, we mention the notion of quantum probability and its basic properties. Next, we propose the axiom of new quantum theory, using the notion of quantum probability. The characteristic property of the quantum state is that the quantum state is determined by the L2-density of the quantum probability distribution of the position variables and the momentum variables of the quantum system. At last, we derive the Schrödinger equations by the reasonable method based on the axiom of new quantum theory. Here we use the variational principle that the real L2-density determining the quantum state of the quantum system, which is, in practice, realized physically, should be determined among the admissible L2-densities so that the energy expectation value takes its stationary value.

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In this article, we established the fundamental principles of new quantum theory. At first, we mention the notion of quantum probability and its basic properties. Next, we propose the axiom of new quantum theory, using the notion of quantum probability. The characteristic property of the quantum state is that the quantum state is determined by the L2-density of the quantum probability distribution of the position variables and the momentum variables of the quantum system. At last, we derive the Schrödinger equations by the reasonable method based on the axiom of new quantum theory. Here we use the variational principle that the real L2-density determining the quantum state of the quantum system, which is, in practice, realized physically, should be determined among the admissible L2-densities so that the energy expectation value takes its stationary value.
Density distribution function of classical statistical mechanics is generally generalized as a product of a general complex function and its complex Hermitian conjugate function, and the average of classical statistical mechanics is generalized as the average of the quantum mechanics. Furthermore, this paper derives three ones of the five axiom presumptions of quantum mechanics, e.g., deduces Schrȍdinger equation by two general ways, makes the three axiom presumptions into three theorems of quantum mechanics, not only solves the crisis to hard understand, but also gets new theories and new discoveries, e.g., this paper solves the crisis of the origin of the wave-particle duality, derives operators, eigenvalues and eigenstates, deduces commutation relations for coordinate and momentum as well as the time and energy, and discovers quantum mechanics is just a generalization ( mechanics ) theory of the complex square root of ( real density function of ) classical statistical mechanics. Quantum mechanics being just a generalization theory of the complex square root of classical statistical mechanics is both new physics and revolutionary discovery, which are affecting people’s deep philosophical thinking for modern physics development, solve all the crisises of quantum mechanics, quantum information and so on, and make quantum mechanics have scientific solid bases being checked and both no basic axiom presumption and no all the quantum strange incomprehensible properties, because classical statistical mechanics and the complex square root of classical statistical mechanics have the scientific solid bases being checked. In addition, this paper discovers the reason no taking the time derivative of space coordinates in Schrȍdinger equation. Therefore, this paper gives solution to the crisis of the first quantization origin, and mainly deduces quantum physics no all the quantum current strange incomprehensible properties.
The Heisenberg uncertainty postulates are a convenient way to describe the qualitative properties of quantum mechanics. The response from Heisenberg’s uncertainty principle is that one can create states that require a certain amount of momentum and position localization. The numerical quantities used by the old Newtonian mechanics, position, momentum, and energy are mere “shadows” of what nature describes: operators. The energy value contradicts the Newtonian notion of any energy level being necessary for a harmonic oscillator. The basic postulates of classical statistical mechanics are now applied to quantum statistical mechanics. In classical mechanics, the variables characterize a microstate that evolves according to the Hamiltonian equations. If the standard deviation relative to what we are interested in is very high, it is probably safe to use the expected value as a classical value. A quantum field theory is a relativistic invariant quantum theory where there is a particular form of quantity operators connected with the classical fields.
The study of quantum statistical mechanics begins with a review of the basic principles of quantum mechanics. Schrödinger’s equation is introduced and Eigenstates (or stationary states) are defined. Model probability for quantum statistics is assumed to have a uniform distribution in phases. Wave functions for many-body systems are defined. The density matrix is introduced. The Planck entropy and the microcanonical ensemble are defined. The differences between classical and quantum statistical mechanics are all based on the differing concepts of a microscopic ‘state’. While the classical microscopic state (specified by a point in phase space) determines the exact position and momentum of every particle, the quantum mechanical state determines neither; quantum states can only provide probability distributions for observable quantities.
In this monograph, the author presents a new approach to non-relativistic quantum mechanics. The monograph has four parts. In Part One the basic results of the theory of probability and of quantum mechanics are established. In Part Two the monadic properties of individual systems are derived from stationary state functions. In Part Three, the collectivistic properties of statistical assemblies are derived from superposed state functions. In Part Four, the experimental methods for determining various physical quantities are mentioned.
Density distribution function of classical statistical mechanics is generally generalized as a product of a general complex function and its complex Hermitian conjugate function, and the average of classical statistical mechanics is generalized as the average of the quantum mechanics. Furthermore, this paper derives three ones of the five axiom presumptions of quantum mechanics, e.g., deduces Schrȍdinger equation by two general ways, makes the three axiom presumptions into three theorems of quantum mechanics, not only solves the crisis to hard understand, but also gets new theories and new discoveries, e.g., this paper solves the crisis of the origin of the wave-particle duality (i.e., complementary principle), derives operators, eigenvalues and eigenstates, deduces commutation relations for coordinate and momentum as well as the time and energy, and discovers quantum mechanics is just a generalization ( mechanics ) theory of the complex square root of ( real density function of ) classical statistical mechanics, which will make people renew thinking modern physics development. In addition, this paper discovers the reason that Schrȍdinger equation doesn’t takes the time derivative of space coordinates. Therefore, this paper gives solution to the Crisis of the first quantization origin.