Related papers: Coulomb problem in NC quantum mechanics: Exact sol…
We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a…
We analyze the effects of noncommutativity in conformal quantum mechanics (CQM) using the $\kappa$-deformed space-time as a prototype. Upto the first order in the deformation parameter, the symmetry structure of the CQM algebra is preserved…
If a quantum mechanical Hamiltonian has an infinite symmetric tridiagonal (Jacobi) matrix form in some discrete Hilbert-space basis representation, then its Green's operator can be constructed in terms of a continued fraction. As an…
It is shown that quantum mechanics is noncontextual if quantum properties are represented by subspaces of the quantum Hilbert space (as proposed by von Neumann) rather than by hidden variables. In particular, a measurement using an…
We consider the quantum dynamics of a harmonic oscillator in noncommutative space under the influence of linearized gravitational waves (GW) in the long wave-length and low-velocity limit. Following the prescription in \cite{ncgw1} we…
In this work we have shown precisely that the curvature of a 2-sphere introduces quantum features in the system through the introduction of the noncommutative (NC) parameter that appeared naturally via equations of motion. To obtain this…
The appearance of noncommuting spatial coordinates is studied in quantum systems containing a magnetic monopole and under the influence of a radial potential. We derive expressions for the commutators of the coordinates that have been…
It is shown that quantum mechanics on noncommutative spaces (NQM) can be obtained by the canonical quantization of some underlying second class constrained system formulated in extended configuration space. It leads, in particular, to an…
The fundamental quantum Coulomb problem in the momentum space is considered. A differential equation with SO(4) simmetry has been obtained in the momentum space instead of the integral Fock equation. The corresponding equation in the…
We present a definition of the two-sided inverse of position operator in general case of deformed Heisenberg algebra leading to minimal length. Energy spectrum and eigenfunctions in momentum space for 1D Coulomb-like potential in deformed…
This article concludes our critical analysis on the role of non-commutativity in quantum theory. After a brief introduction of the necessary notions on point processes, we re-analyse model B proposed in "On non-commutativity in quantum…
Quantum mechanics is often developed in the position representation, but this is not necessary, and one can perform calculations in a representation-independent fashion, even for wavefunctions. In this work, we illustrate how one can…
A new approach in solution of simple quantum mechanical problems in deformed space with minimal length is presented. We propose the generalization of Schro\"edinger equation in momentum representation on the case of deformed Heisenberg…
The Coulomb gauge has at least two advantadges over other gauge choices in that bound states between quarks and studies of confinement are easier to understand in this gauge. However, perturbative calculations, namely Feynman loop…
The Variational Quantum Eigensolver approach to the electronic structure problem on a quantum computer involves measurement of the Hamiltonian expectation value. Formally, quantum mechanics allows one to measure all mutually commuting or…
The response of a test particle, both for the free case and under the harmonic oscillator potential, to circularly polarized gravitational waves is investigated in a noncommutative quantum mechanical setting. The system is quantized…
Having started with the general formulation of the quantum theory of the real scalar field (QFT) in the general Riemannian space--time $ V_{1,3} $, the general--covariant quasinonrelativistic quantum mechanics of a point-like spinless…
We are interested in the similarities and differences between the quantum-classical (Q-C) and the noncommutative-commutative (NC-Com) correspondences. As one useful platform to address this issue we derive the superstar Wigner-Moyal…
In this article we have investigated some of the theoretical aspects of the solutions of quantum mechanical equations in Rindler space. We have developed the formalism for exact analytical solutions for Schr$\ddot{\rm{o}}$dinger equation…
In our previous work we have constructed a model of noncommutative (NC) gravity based on $SO(2,3)_\star$ gauge symmetry. In this paper we extend the model by adding matter fields: fermions and a $U(1)$ gauge field. Using the enveloping…