In this paper, we try to construct the famous Schrodinger equation of quantum mechanics in a very simple manner. It is shown that, even though the mathematical procedure of the construction may be correct, it is evident that the establishment of the Schrodinger equation is unreasonable in physics. We point out the application of the Schrodinger equation, in fact, will lead to the transformation of the studied system into an arbitrary variable pseudo physical system. This finding may help to uncover the nature of the nonlocality and Heisenberg's uncertainty principle of quantum mechanics. It is inevitable that the use of the Schrodinger equation will violate the law of conservation of energy. Hence, we argue that the Schrodinger equation is unsuitable to be applied to any physical systems.
In this paper, we try to construct the famous Schrodinger equation of quantum mechanics in a very simple manner. It is shown that, even though the mathematical procedure of the construction may be correct, it is evident that the establishment of the Schrodinger equation is unreasonable in physics. We point out the application of the Schrodinger equation, in fact, will lead to the transformation of the studied system into an arbitrary variable pseudo physical system. This finding may help to uncover the nature of the nonlocality and Heisenberg's uncertainty principle of quantum mechanics. It is inevitable that the use of the Schrodinger equation will violate the law of conservation of energy. Hence, we argue that the Schrodinger equation is unsuitable to be applied to any physical systems.
This article establishes the proof of the Schrödinger equation for numerous quantum systems, utilizing Heisenberg's uncertainty principle. The Fourier transform connects functions in the time and frequency domains, resulting in the mathematical inequality that is the foundation of the uncertainty principle. In the part of Methods and Theory, the article derives the uncertainty principle through Fourier transforms by defining the mean and variance of angular frequency and time, and subsequently expanding the integral. This establishes the fundamental connection between time and frequency domains, illustrating the constraints imposed by quantum mechanics. In the part of Results and Application, the article applies the uncertainty principle to derive the Schrödinger equation under different conditions: free particle, particle in a box, harmonic oscillator, and hydrogen atom. For each case, the article assumes wave function solutions, uses the uncertainty in position and momentum to estimate kinetic and potential energies, and shows that the total energy matches the ground state energy derived from the Schrödinger equation. The results highlight the critical role of Heisenberg's uncertainty principle in understanding key aspects of quantum mechanics, providing a unified framework for these diverse systems.
This paper is intended to show the Schrodinger equation, within its structure, allows the manifestation of the wave function collapse within a very natural way of reasoning. In fact, as we will see, nothing new must be inserted to the classical quantum mechanics, viz., only the dialectics of the physical world must be interpreted under a correct manner. We know the nature of a physical system turns out to be quantical or classical, and, once under the validity of the Schrodinger equation to provide the evolution of this physical system, the dialectics, quantum or classical, mutually exclusive, must also be under context through the Schrodinger equation, issues within the main scope of this paper. We will show a classical measure, the obtention of a classical result, emerges from the structure of the Schrodinger equation, once one demands the possibility that, over a chronological domain, the system begins to provide a classical dialectic, showing the collapse may be understood from both: the structure of the Schrodinger equation as well as from the general solution to this equation. The general solution, even with a dialectical change of description, leads to the conservation of probability, obeying the Schrodinger equation. These issues will turn out to be a consequence of a general potential energy operator, obtained in this paper, including the possibility of the classical description of the physical system, including the possibility of interpretation of the collapse of the quantum mechanical state vector within the Schrodinger equation scope.
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.
This paper is intended to show the Schrodinger equation, within its structure, allows the manifestation of the wave function collapse within a very natural way of reasoning. In fact, as we will see, nothing new must be inserted to the classical quantum mechanics, viz., only the dialectics of the physical world must be interpreted under a correct manner. We know the nature of a physical system turns out to be quantical or classical, and, once under the validity of the Schrodinger equation to provide the evolution of this physical system, the dialectics, quantum or classical, mutually exclusive, must also be under context through the Schrodinger equation, issues within the main scope of this paper. We will show a classical measure, the obtention of a classical result, emerges from the structure of the Schrodinger equation, once one demands the possibility that, over a chronological domain, the system begins to provide a classical dialectic, showing the collapse may be understood from both: the structure of the Schrodinger equation as well as from the general solution to this equation. The general solution, even with a dialectical change of description, leads to the conservation of probability, obeying the Schrodinger equation. These issues will turn out to be a consequence of a general potential energy operator, obtained in this paper, including the possibility of the classical description of the physical system, including the possibility of interpretation of the collapse of the quantum mechanical state vector within the Schrodinger equation scope.
Ever since Schrodinger, the time-dependent Schrodinger equation has been regarded as the fundamental physical law of the unitary-only quantum theory. However, while the origin of time for non-conservative systems can be traced back to the environmental influence, this procedure is inapplicable for the closed (conservative) quantum systems. Hence the question of the origin of time for closed systems. In addressing this issue, in order to avoid circularity of the standard universal (global) time as well as assumptions that could be additional to the standard postulates of quantum theory, we stick to the so-called quantum-mechanical local time. The problems that inevitably appear in such minimalist rejection of the standard role of time in physics are solved with mathematical rigor while leading to the emergent time for every, at least approximately, closed (conservative) system as well as to establishing the time-dependent Schrodinger law as the fundamental law of the unitary non-relativistic as well as relativistic-field quantum theory.
One of the advantages of a reconstruction of quantum mechanics based on transparent physical axioms is that it may offer insight to naturally generalize quantum mechanics by relaxing the axioms. Here, we discuss possible extensions of quantum mechanics within a general epistemic framework based on an operational scheme of estimation of momentum given information on the conjugate positions under epistemic restriction. The epistemic restriction is parameterized by a global-nonseparable random variable on the order of Planck constant, an ontic extension to the separable classical phase-space variables. Within the estimation scheme, the canonical quantum laws are reconstructed for a specific estimator and estimation error. In the present work, keeping the Born's quadratic law intact, we construct a class of nonlinear variants of Schr\"odinger equation and generalized Heisenberg uncertainty principle within the estimation scheme by assuming a more general class of estimation errors. The nonlinearity of the Schr\"odinger equation and the deviation from the Heisenberg uncertainty principle thus have a common transparent operational origin in terms of generalizations of estimation errors. We then argue that a broad class of nonlinearities and deviations from the Heisenberg uncertainty principle arise from estimation errors violating a plausible inferential-causality principle of estimation independence which is respected by the standard quantum mechanics. This result therefore constrains possible extensions of quantum mechanics and suggests directions to generalize quantum mechanics which comply with the principle of estimation independence.