Related papers: On the quantum spectrum of isochronous potentials
We continue our work on the study of spherically symmetric loop quantum gravity coupled to two spherically symmetric scalar fields, one which acts as a clock. As a consequence of the presence of the latter, we can define a true Hamiltonian…
Using a recent reformulation of quantum mechanics where the potential function is not required, we are able to obtain the energy spectrum and wave function associated with the infinite square well analytically. Therefore, this work…
The function exp(iwt) describes an oscillating motion. Energy of the oscillator is proportional to the square of w. exp(iwt) is the solution of a differential equation. We have replaced this differential equation by the corresponding…
We study different quantum one dimensional systems with noncanonical commutation rule $[x,p]=i\hbar (1+sH),$ where $H$ is the one particle Hamiltonian and $s$ is a parameter. This is carried-out using semiclassical arguments and the surmise…
We perform a systematic WKB expansion to all orders for a one-dimensional system with potential $V(x)=U_0/\cos^2{(\alpha x)}$. We are able to sum the series to the exact energy spectrum. Then we show that at any finite order the error of…
A family of quantum anharmonic oscillators is studied in any finite spatial dimension in the scheme of first quantization and the investigation of their eigenenergies is presented. The statistical properties of the calculated eigenenergies…
The transformation of a classical system into its quantum counterpart is usually done through the well known procedure of canonical quantization. However, on non-Cartesian domains, or on bounded Cartesian domains, this procedure can be…
This paper presents the first-order supersymmetric rational extension of the quantum anisotropic harmonic oscillator (QAHO) in multiple dimensions, including full-line, half-line, and their combinations. The exact solutions are in terms of…
The origin of the identical gamma-ray energies (IB) observed in the K=33/2$^+$ and K=16$^+$ bands in $^{177}$Lu and $^{178}$Hf respectively is investigated using deformed Hartree-Fock and Angular Momentum Projection technique. We find that…
Being attracted by the property of classical polar code, researchers are trying to find its analogue in quantum fields, which is called quantum polar code. The first step and the key to design quantum polar code is to find out for the…
In this work, we delve into the theory of sheared potentials in non-relativistic quantum mechanics. After defining what we mean by a family of sheared potentials, we consider these families in two particular but emblematic cases, the…
Macroscopic ensembles of radiating dipoles are ubiquitous in the physical and natural sciences. In the classical limit the dipoles can be described as damped-driven oscillators, which are able to spontaneously synchronize and collectively…
The Schroedinger eigenvalue problems for the Whittaker-Hill potential $Q_{2}(x)=\tfrac{1}{2} h^2\cos4x+4h\mu\cos2x$ and the periodic complex potential $Q_{1}(x)=\tfrac{1}{4}h^2{\rm e}^{-4ix}+2h^2\cos2x$ are studied using their realizations…
We derive the energy levels associated with the even-parity wave functions of the harmonic oscillator with an additional delta-function potential at the origin. Our results bring to the attention of students a non-trivial and analytical…
We develop a semiclassical framework for studying quantum particles constrained to curved surfaces using the momentous quantum mechanics formalism, which extends classical phase-space to include quantum fluctuation variables (moments). In a…
Phase-space features of the Wigner flow for an anharmonic quantum system driven by the harmonic oscillator potential modified by the addition of an inverse square (one-dimension Coulomb-like) contribution are analytically described in terms…
We study classical and quantum maps on the torus phase space, in the presence of noise. We focus on the spectral properties of the noisy evolution operator, and prove that for any amount of noise, the quantum spectrum converges to the…
A correspondence is established between measure-preserving, ergodic dynamics of a classical harmonic oscillator and a quantum mechanical gauge theory on two-dimensional Minkowski space. This correspondence is realized through an isometric…
While $(2+1)$-dimensional black holes in the Einstein theory allow for only the anti-de Sitter asymptotic, when the higher curvature correction is tuned on, the asymptotically flat, de Sitter and anti-de Sitter cases are included. Here we…
The 1-D dimension harmonic oscillator in Snyder space is investigated in its classical and quantum versions. The classical trajectory is obtained and the semiclassical quantization from the phase space trajectories is discussed. In the…