Related papers: Schr\"odinger equation of general potential
The nonlinear Schrodinger equation is well known as a universal equation in the study of wave motion. In the context of wave motion at the free surface of an incompressible fluid, the equation accurately predicts the evolution of modulated…
In this paper we suggest a natural interpretation of the de Broglie-Bohm quantum potential, as the energy due to the oscillating electromagnetic field (virtual photon) coupled with moving charged particle. Generalization of the…
Since the advent of quantum mechanics different approaches to find analytical solutions of the Schr\"odinger equation have been successfully developed. Here we follow and generalize the approach pioneered by Natanzon and others by which the…
We show in this paper that the basic representations of position and momentum in a quantum mechanical system, that are guided by a generalized uncertainty principle and lead to a corresponding one-parameter eigenvalue problem, can be…
This paper posits the existence of, and finds a candidate for, a variable change that allows quantum mechanics to be interpreted as quantum geometry. The Bohr model of the Hydrogen atom is thought of in terms of an indeterministic electron…
We present a variational approach which shows that the wave functions belonging to quantum systems in different potential landscapes, are pairwise linked to each other through a generalized continuity equation. This equation contains a…
The formalism of quantum mechanics is presented in a way that its interpretation as a classical field theory is emphasized. Two coupled real fields are defined with given equations of motion. Densities and currents associated to the fields…
A previous derivation of the single-particle Schr\"odinger equation from statistical assumptions is generalized to an arbitrary number $N$ of particles moving in three-dimensional space. Spin and gauge fields are also taken into account. It…
The aim of the lecture is to briefly describe the mathematical background of scattering theory for two- and three-particle quantum systems. We discuss basic objects of the theory: wave and scattering operators and the corresponding…
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 Laplace transform is a valuable tool in physics, particularly in solving differential equations with initial or boundary conditions. A 2014 study by Tsaur and Wang (2014 \emph{Eur.~J.~Phys.} \textbf{35} 015006) introduced a…
In quantum mechanics textbooks, a single-particle scattering theory is introduced. In the present work, a generalized scattering theory is presented, which can be in principle applied to the scattering problems of arbitrary number of…
The local phase-invariance of the momentum-space Schr\"odinger equation for free-particle has been used to construct quantum kinematics that describes a motion of the particle in external U(1) background gauge field. The gauge structure…
Following the spirit of de Broglie and Einstein, we think the concepts of matter and radiation can be unified. We know a particle propagates like a wave; its motion is described by certain wave equations. At this point, it is not clear what…
Some recent experiments claim to show that any model in which a quantum state represents mere information about an underlying physical reality of the system must make predictions which contradict those of quantum theory. The present work…
In 1926, Erwin Schrodinger wrote a series of papers that invented wave mechanics and set the foundation for much of the single-particle quantum mechanics that we teach today. In his first paper, he solved the Schrodinger equation using the…
A quaternionic wavefunction consisting of real and scalar functions is found to satisfy the quaternionic momentum eigenvalue equation. Each of these components are found to satisfy a generalized wave equation of the form…
An universal exact description of kinetics of open quantum systems in terms of random wave functions and stochastic Schr\"{o}dinger equation is suggested. It is shown that evolution of random quantum states of an open system is unitary on…
We show that the quantum wavefunction, interpreted as the probability density of finding a single non-localized quantum particle, which evolves according to classical laws of motion, is an intermediate description of a material quantum…
The Poincar\'e symmetry can be contracted in two ways to yield the Galilei symmetry and the Carroll symmetry. The well-known Schr\"odinger equation exhibits the Galilei symmetry and is a fundamental equation in Galilean quantum mechanics.…