Related papers: Schr\"odinger equation of general potential
This paper is the first of two papers devoted to formulation of quantum mechanics of a particle in a normal geodesic frame of reference in the general Riemannian space-time. Here canonical quantization of geodesic motion in the…
The quantum mechanical time-evolution is studied for a particle under the influence of an explicitly time-dependent rotating potential. We discuss the existence of the propagator and we show that in the limit of rapid rotation it converges…
The use of operator methods of algebraic nature is shown to be a very powerful tool to deal with different forms of relativistic wave equations. The methods provide either exact or approximate solutions for various forms of differential…
It is shown that analytically soluble bound states of the Schr\"odinger equation for a large class of systems relevant to atomic and molecular physics can be obtained by means of the Laplace transform of the confluent hypergeometric…
An analysis is made of the relation between quantum theory and classical mechanics, in the context of the limit $\hbar \to 0$. Several ways in which this limit may be performed are considered. It is shown that Schr\"odinger's equation for a…
The derivation of the Schr\"odinger-like equations from the system of equations of the quantum hydrodynamic analogy (QHA) is analyzed in presence of fluctuations. If in absence of fluctuation each QHA solution can be tracked back to the…
An universal form of kinetic equation for open systems is considered which naturally unifies classical and quantum cases and allows to extend concept of wave function to open quantum systems. Corresponding stochastic Schr\"{o}dinger…
The angular part of the Schrodinger equation for a central potential is brought to the one-dimensional 'Schrodinger form' where one has a kinetic energy plus potential energy terms. The resulting polar potential is seen to be a family of…
We develop the general theory of spinning particles with electric and magnetic dipole moments moving in arbitrary electromagnetic, inertial and gravitational fields. Both the quantum-mechanical and classical dynamics is investigated. We…
We construct a new nonlinear deformed Schr\"odinger structure using a nonlinear derivative operator which depends on a parameter $q$. This operator recovers Newton derivative when $q \rightarrow 1$. Using this operator we propose a deformed…
This study introduces the quantum force wave equation (QFWE) as a general theory of quantum forces, a novel framework that redefines quantum forces as emergent phenomena arising from the interaction between quantum particles and curved…
We apply the many-particle Schr\"{o}dinger-Newton equation, which describes the co-evolution of an many-particle quantum wave function and a classical space-time geometry, to macroscopic mechanical objects. By averaging over motions of the…
With a q-deformed quantum mechanical framework, features of the uncertainty relation and a novel formulation of the Schr\"odinger equation are considered.
Schwinger's quantization scheme is extended in order to solve the problem of the formulation of quantum mechanics on a space with a group structure. The importance of Killing vectors in a quantization scheme is showed. Usage of these…
We derive the Schroedinger equation for a spinless charged particle constrained to a curved surface with electric and magnetics fields applied. The particle is confined on the surface using a thin-layer procedure, giving rise to the…
We introduce the third five-parametric ordinary hypergeometric energy-independent quantum-mechanical potential, after the Eckart and P\"oschl-Teller potentials, which is proportional to an arbitrary variable parameter and has a shape that…
We solve the one-dimensional Schr\"odinger equation for the bound states of two potential models with a rich structure as shown by their "spectral phase diagram". These potentials do not belong to the well-known class of exactly solvable…
We derive new solutions of the Schr\"odinger equation which describe the motion of particles in the Penning trap. These solutions are direct counterparts of classical orbits. They are obtained by injection of classical trajectories into the…
The possibility of consistency between the basic quantum principles and reduction (wave function reduction) is reexamined. The mathematical description of an organized macroscopic device is constructed explicitly as a convenient tool for…
This work deals with Schr\"odinger equations with quadratic and sub-quadratic Hamiltonians perturbed by a potential. In particular we shall focus on bounded, but not necessarily smooth perturbations. We shall give a representation of such…