Related papers: Few quantum mechanical models in higher dimension-…
An operator-valued quantum phase space formula is constructed. The phase space formula of Quantum Mechanics provides a natural link between first and second quantization, thus contributing to the understanding of quantization problem. By…
Partial differential equation (PDE) models with multiple temporal/spatial scales are prevalent in several disciplines such as physics, engineering, and many others. These models are of great practical importance but notoriously difficult to…
This study explores the influence of a Stark-like perturbative potential on a quantum particle confined to a cylindrical surface (QPCS) and its implications for extra-dimensional theories. The QPCS framework is particularly relevant to…
In a way paralleling the recently accepted non-Hermitian version of quantum mechanics in its Schr\"{o}dinger representation (working often with the innovative and heuristically productive concept of ${\cal PT}-$symmetry), it is demonstrated…
Algorithms are described for efficiently simulating quantum mechanical systems on quantum computers. A class of algorithms for simulating the Schrodinger equation for interacting many-body systems are presented in some detail. These…
We consider the ADM splitting of the Einstein-Hilbert action in five dimensions in the presence of matter that can be either a "point particle", or a set of scalar fields. The Hamiltonian, being a linear superposition of constraints, is…
In this paper we describe the integral transform that allows to write solutions of one partial differential equation via solution of another one. This transform was suggested by the author in the case when the last equation is a wave…
The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average…
One-dimensional nonrelativistic systems are studied when time-independent potential interactions are involved. Their supersymmetries are determined and their closed subsets generating kinematical invariance Lie superalgebras are pointed…
We show that the so called Elko equation can be derived from a 5-dimensional Dirac equation. We argue that this result can be relevant for dark matter and cosmological scenarios. We generalize our procedure to higher dimensions.
Exact analytical, closed-form solutions, expressed in terms of special functions, are presented for the case of a three-dimensional nonlinear quantum oscillator with a position dependent mass. This system is the generalization of the…
We present a new six-parameter family of potentials whose solutions are expressed in terms of the hypergeometric functions 3F2, 2F2 and 1F2. Both the scattering data and the bound states of these potentials are explicitly computed and the…
The quantum field theory of extended objects is employed to address the hitherto nonrenormalizable Pauli interaction. This is achieved by quantizing the Dirac field using the infinite dimensional generalization of the extended object…
We investigate modifications of quantum mechanics (QM) that replace the unitary group in a finite dimensional Hilbert space with a finite group and determine the minimal sequence of subgroups necessary to approximate QM arbitrarily closely…
After a brief discussion of the meaning of the potential in quantum mechanics, we examine the results of the Yukawa model (scalar meson exchange) for the nucleon-nucleon interaction in three different dynamical frameworks: the…
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…
The importance of the energy spectrum of bound states and their restrictions in quantum mechanics due to the different methods have been used for calculating and determining the limit of them. Comparison of Schrodinger-like equation…
A closed form solution for the one-dimensional Schr\"{o}dinger equation with a finite number of $\delta$-interactions \[ \mathbf{L}_{q,\mathfrak{I}_{N}}y:=-y^{\prime\prime}+\left( q(x)+\sum _{k=1}^{N}\alpha_{k}\delta(x-x_{k})\right)…
In this paper we present the first steps for obtaining a discrete Quantum Mechanics making use of the Umbral Calculus. The idea is to discretize the continuous Schroedinger equation substituting the continuous derivatives by discrete ones…
We generalize a recently proposed algebraic method in order to treat non-Hermitian Hamiltonians. The approach is applied to several quadratic Hamiltonians studied earlier by other authors. Instead of solving the Schr\"odinger equation we…