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By using the complete solution of the Milburn equation (beyond the Lindblad form that it is generally used) that describes intrinsic decoherence, we study the decaying dynamics of a displaced harmonic oscillator. We calculate the…

Quantum Physics · Physics 2022-04-08 Alejandro R. Urzúa , Héctor M. Moya-Cessa

Experimental results from literature show equidistant energy levels in thin Bi films on surfaces, suggesting a harmonic oscillator description. Yet this conclusion is by no means imperative, especially considering that any measurement only…

Quantum Physics · Physics 2021-07-20 Fabian Teichert , Eduard Kuhn , Angela Thränhardt

The single well 1D harmonic oscillator is one of the most fundamental and commonly solved problems in quantum mechanics. Traditionally, in most introductory quantum mechanics textbooks, it is solved using either a power series method, which…

Quantum Physics · Physics 2024-01-17 Mate Garai , Douglas A. Barlow

An exact solution of the energy shift in each quantum mechanical energy levels in a one dimensional symmetrical linear harmonic oscillator has been investigated. The solution we have used here is firstly derived by manipulating Schrodinger…

Quantum Physics · Physics 2007-05-23 Hendry I. Elim

In this work, the analytical solutions of the $D$-dimensional Schr\"odinger equation are studied in great detail for the Wood-Saxon potential by taking advantage of the Pekeris approximation. Within a novel improved scheme to surmount…

Quantum Physics · Physics 2018-01-22 V. H. Badalov

In this note we consider high energy eigenfunctions of the harmonic oscillator in $\mathbb{R}^d$ and prove that any invariant measure on the energy surface can be written as a weak limit of eigenfunctions.

Analysis of PDEs · Mathematics 2020-01-28 Elie Studnia

We consider the system of two interacting atoms confined in axially symmetric harmonic trap. Within the pseudopotential approximation, we solve the Schroedinger equation exactly, discussing the limits of quasi-one and quasi-two-dimensional…

Quantum Physics · Physics 2009-11-10 Z. Idziaszek , T. Calarco

Analytic and approximate solutions for the energy eigenvalues generated by a confined softcore Coulomb potentials of the form a/(r+\beta) in d>1 dimensions are constructed. The confinement is effected by linear and harmonic-oscillator…

Mathematical Physics · Physics 2015-06-22 Richard L Hall , Nasser Saad

We investigate the behaviour of a two-dimensional harmonic oscillator in an elastic medium that possesses a spiral dislocation (an edge dislocation). We show that the Schr\"odinger equation for harmonic oscillator in the presence of a…

Quantum Physics · Physics 2018-01-17 A. V. D. M. Maia , K. Bakke

By the method of generalized spherical harmonic polynomials, the Schr\"{o}dinger equation for a four-body system in $D$-dimensional space is reduced to the generalized radial equations where only six internal variables are involved. The…

Atomic Physics · Physics 2009-11-10 Xiao-Yan Gu , Zhong-Qi Ma , Jian-Qiang Sun

We study the system of two ultracold atoms in a three-dimensional (3D) or two-dimensional (2D) completely anisotropic harmonic trap. We derive the algebraic equation J_{3D}(E) = 1/a_{3D} (J_{2D}(E) = ln a_{2D}) for the eigen-energy E of…

Atomic and Molecular Clusters · Physics 2020-05-20 Yue Chen , Da-Wu Xiao , Ren Zhang , Peng Zhang

A nonpolynomial one-dimensional quantum potential representing an oscillator, that can be considered as placed in the middle between the harmonic oscillator and the isotonic oscillator (harmonic oscillator with a centripetal barrier), is…

Quantum Physics · Physics 2010-11-16 J. F. Cariñena , A. M. Perelomov , M. F. Rañada , M. Santander

We present closed analytical expressions for the particle and kinetic energy spatial densities at finite temperatures for a system of noninteracting fermions (bosons) trapped in a d-dimensional harmonic oscillator potential. For d=2 and 3,…

Statistical Mechanics · Physics 2009-11-07 Brandon P. van Zyl , Rajat K. Bhaduri , Akira Suzuki , Matthias Brack

In this paper we have obtained the exact eigenstates of a two dimensional damped harmonic oscillator in time dependent noncommutative space. It has been observed that for some specific choices of the damping factor and the time dependent…

Quantum Physics · Physics 2020-12-09 Manjari Dutta , Shreemoyee Ganguly , Sunandan Gangopadhyay

We study the eigen-energy and eigen-function of a quantum particle acquiring the probability density-dependent effective mass (DDEM) in harmonic oscillators. Instead of discrete eigen-energies, continuous energy spectra are revealed due to…

Pattern Formation and Solitons · Physics 2021-06-01 Jen-Hsu Chang , Chun-Yan Lin , Ray-Kuang Lee

We consider the $q$-deformed Schr\"odinger equation of the harmonic oscillator on the $N$-dimensional quantum Euclidian space. The creation and annihilation operator are found, which systematically produce all energy levels and…

High Energy Physics - Theory · Physics 2011-07-19 Ursula Carow-Watamura , Satoshi Watamura

We investigate the energy spectrum and the corresponding eigenfunctions of a 2D Dirac oscillator confined by an antidot potential in the presence of a magnetic field and Aharonov-Bohm flux field. Analytical solutions are obtained and…

Quantum Physics · Physics 2016-11-22 Huseyin Akcay , Ramazan Sever

We present a supersymmetric analysis for the d-dimensional Schroedinger equation with the generalized isotonic nonlinear-oscillator potential V(r)={B^2}/{r^{2}}+\omega^{2} r^{2}+2g{(r^{2}-a^{2})}/{(r^{2}+a^{2})^{2}}, B\geq 0. We show that…

Mathematical Physics · Physics 2011-03-28 Richard L. Hall , Nasser Saad , Ozlem Yesiltas

In this paper we study the (2 + 1)-dimensional Dirac oscillator in the noncommutative phase space and the energy eigenvalues and the corresponding wave functions of the system are obtained through the sl(2) algebraization. It is shown that…

High Energy Physics - Theory · Physics 2017-10-11 H. Panahi , A. Savadi

We study the effects of Snyder-de Sitter commutation relations on relativistic bosons by solving analytically in the momentum space representation the Klein-Gordon oscillator in arbitrary dimensions. The exact bound states spectrum and the…

Quantum Physics · Physics 2021-02-16 Zoubir Hemame , Mokhtar Falek , Mustafa Moumni