相关论文: How do I introduce Schr\"odinger equation during t…

This paper introduces a novel deep-learning-based approach for numerical simulation of a time-evolving Schr\"odinger equation inspired by stochastic mechanics and generative diffusion models. Unlike existing approaches, which exhibit…

A nonlinear wave mechanical equation is proposed by inserting an imaginary quantum potential into the Schr\"{o}dinger equation. An explicit expression for its solution is given under certain assumptions and it is shown that it entails…

Landau and Peierls wrote down the Hamiltonian of a simplified version of quantum electrodynamics in the particle-position representation. We present a multi-time version of their Schr\"odinger equation, which bears several advantages over…

The Schrodinger equation is a mathematical equation describing the wave function's behavior in a quantum-mechanical system. It is a partial differential equation that provides valuable insights into the fundamental principles of quantum…

The de Broglie - Bohm "pilot-wave" theory replaces the paradoxical wave-particle duality of ordinary quantum theory with a more mundane and literal kind of duality: each individual photon or electron comprises a quantum wave (evolving in…

We propose an interpretative framework for quantum mechanics corresponding to the specifications of Louis de Broglie's double-solution theory. The principle is to decompose the evolution of a quantum system into two wave functions: an…

We address the issue of the relation between the canonical functional Schr\"odinger representation in quantum field theory and the approach of precanonical field quantization proposed by the author, which requires neither a distinguished…

The functional Schr\"odinger equation in curved space-time is derived from the manifestly covariant precanonical Schr\"odinger equation. The Schr\"odinger wave functional is expressed as the trace of the multidimensional product integral of…

All the concepts and principles necessary to understand quantum mechanics on an initial level are given in a form suitable for the non-expert. The concepts explained include visualizing the wave function, wave-particle duality, the…

The photoelectric effect has been discovered by H. Hertz, and studied experimentally by P. Lenard. First theoretical explanation has been done by A. Einstein who suggested the corpuscular theory of light introducing the "photons" which are…

We consider the special and general relativistic extensions of the action principle behind the Schr\"odinger equation distinguishing classical and quantum contributions. Postulating a particular quantum correction to the source term in the…

The main goal of this brief report is to provide some new insight into how promising the Schroedinger-Newton equation would be to explain the emergence of classicality. Based on the similarity of the Newton and Coulomb potentials, we add an…

We present quantum algorithms for electromagnetic fields governed by Maxwell's equations. The algorithms are based on the Schr\"odingersation approach, which transforms any linear PDEs and ODEs with non-unitary dynamics into a system…

We revisit the Schr\"{o}dinger equation of a quantum particle that is confined on a curved surface. Inspired by the novel work of R. C. T. da Costa [1] we find the field equation in a more convenient notation. The contribution of the…

This paper is about the surprising connection between the Fourier heat equation and the Schr\"odinger wave equation. In fact, if the independent "time" variable in the heat equation is replaced by the time variable multiplied by…

A duality between an electrostatic problem in a three dimensional world and a quantum mechanical problem in a one dimensional world which allows one to obtain the ground state solution of the Schr\"odinger equation by using electrostatic…

Time flow has been embodied in time-dependent Schroedinger equation representing one of the foundations of quantum mechanics. Pauli's criticism (1933) has, however, indicated that the assumptions concerning representation Hilbert space have…

In this article we discuss a procedure to solve the one dimensional (1D) Schroedinger Equation for a periodic potential, which may be well suited to teach band structure theory. The procedure is conceptually very simple, so that it may be…

The paper shows the relationship between the major wave equations in quantum mechanics and electromagnetism, such as Schroedinger's equation, Dirac's equation and the Maxwell equations. It is shown that they can be derived in a striking…

In this article, we investigate Bohm's view of quantum theory, especially Bohm's quantum potential, from a new perspective. We develop a quasi-Newtonian approach to Bohmian mechanics. We show that to arrive at Bohmian formulation of quantum…