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The approximation of the eigenvalues and eigenfunctions of an elliptic operator is a key computational task in many areas of applied mathematics and computational physics. An important case, especially in quantum physics, is the computation…
In present article the self-contained derivation of eigenvalue inverse problem results is given by using a discrete approximation of the Schroedinger operator on a bounded interval as a finite three-diagonal symmetric Jacobi matrix. This…
In this work we study the Schr\"{o}dinger equation in the presence of the Hartmann potential with a generalized uncertainty principle. We pertubatively obtain the matrix elements of the hamiltonian at first order in the parameter of…
Minimization of the expectation value of energy under the constraints imposed by the uncertainty principle can be a convenient method of solving quantum-mechanical problems.
In this study, we solve the Klein-Gordon equation with equal scalar and vector q-deformed hyperbolic modified P\"{o}schl-Teller potential. The explicit expressions of bound state spectra and the normalized eigenfunctions for s-wave bound…
Recently one and two-parameter deformed Einstein equations have been studied for extremal quantum black holes which have been proposed to obey deformed statistics by Strominger. In this study, we give a deeper insight to the deformed…
The relativistic equivalent of the Schr\"odinger equation for a two particle bound state having the total angular momentum $S$ is written in the form of a Lorentz covariant set of equations (p_1^mu+p_2^mu+Omega^mu)Psi(p_1,p_2;P)…
The aim of this paper is to find out how would possible space non-commutativity (NC) alter the QM solution of the Coulomb problem. The NC parameter lambda is to be regarded as a measure of the non-commutativity - setting lambda = 0 means a…
We consider the Schr\"odinger equation for hydrogen-like atom with Coulomb potential and non-point ball nucleus. The eigenvalues and eigenfunctions of the operator given by an arbitrary rotation-invariant boundary value problem on the…
We study the valence electron of an alkaline atom or a general charged particle with arbitrary spin and with magnetic moment moving in a rotating magnetic field. By using a time-dependent unitary transformation, the Schr\"odinger equation…
In the framework of the deformed quantum mechanics with minimal length, we consider the motion of a non-relativistic particle in a homogeneous external field. We find the integral representation for the physically acceptable wave function…
The Legendre transform expresses dynamics of a classical system through first-order Hamiltonian equations. We consider coherent state transforms with a similar effect in quantum mechanics: they reduce certain quantum Hamiltonians to…
Quantum--mechanical operators corresponding to canonical momentum and position of a point--like particle, which follow from the quantum field theory in the general Riemannian space-time, satisfy generally to a deformation of the canonical…
The full spectrum and eigenfunctions of the quantum version of a nonlinear oscillator defined on an N-dimensional space with nonconstant curvature are rigorously found. Since the underlying curved space generates a position-dependent…
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…
A systematic study of deformations of four-dimensional Einsteinian space-times embedded in a pseudo-Euclidean space $E^N$ of higher dimension is presented. Infinitesimal deformations, seen as vector fields in $E^N$, can be divided in two…
Recently, [10,11], the Heisenberg Uncertainty relation and the No-Cloning property in Quantum Mechanics and Quantum Computation, respectively, have been extended to versions of Quantum Mechanics and Quantum Computation which are…
Using a simple geometrical construction based upon the linear action of the Heisenberg--Weyl group we deduce a new nonlinear Schr\"{o}dinger equation that provides an exact dynamic and energetic model of any classical system whatsoever, be…
We explore some explicit representations of a certain stable deformed algebra of quantum mechanics, considered by R. Vilela Mendes, having a fundamental length scale. The relation of the irreducible representations of the deformed algebra…
We study the problem of the attractive inverse square potential in quantum mechanics with a generalized uncertainty relation. Using the momentum representation, we show that this potential is regular in this framework. We solve analytically…