scholarly journals Discrete Quantum Harmonic Oscillator

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1362
Author(s):  
Alina Dobrogowska ◽  
David J. Fernández C.
Keyword(s):  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Discrete Model ◽  
Schrodinger Equation ◽  
Factorization Method ◽  
Quantum Harmonic Oscillator ◽  
Meixner Polynomials

In this paper, we propose a discrete model for the quantum harmonic oscillator. The eigenfunctions and eigenvalues for the corresponding Schrödinger equation are obtained through the factorization method. It is shown that this problem is also connected with the equation for Meixner polynomials.

Effective mass of the discrete values as a hidden feature of the one-dimensional harmonic oscillator model: Exact solution of the Schrödinger equation with a mass varying by position

2021 ◽  
pp. 2150206
Author(s):  
E. I. Jafarov ◽  
S. M. Nagiyev
Keyword(s):  
Energy Spectrum ◽  
Positive Integer ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Effective Mass ◽  
Schrodinger Equation ◽  
Solvable Model ◽  
Wave Functions ◽  
Stationary States ◽  
Quantum Harmonic Oscillator

In this paper, exactly solvable model of the quantum harmonic oscillator is proposed. Wave functions of the stationary states and energy spectrum of the model are obtained through the solution of the corresponding Schrödinger equation with the assumption that the mass of the quantum oscillator system varies with position. We have shown that the solution of the Schrödinger equation in terms of the wave functions of the stationary states is expressed by the pseudo Jacobi polynomials and the mass varying with position depends from the positive integer [Formula: see text]. As a consequence of the positive integer [Formula: see text], energy spectrum is not only non-equidistant, but also there are only a finite number of energy levels. Under the limit, when [Formula: see text], the dependence of effective mass from the position disappears and the system recovers known non-relativistic quantum harmonic oscillator in the canonical approach where wave functions are expressed by the Hermite polynomials.

scholarly journals Quantum harmonic oscillator with time-dependent mass

2018 ◽  
Vol 32 (20) ◽  
pp. 1850235 ◽  
Author(s):  
I. Ramos-Prieto ◽  
A. Espinosa-Zuñiga ◽  
M. Fernández-Guasti ◽  
H. M. Moya-Cessa
Keyword(s):  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Schrodinger Equation ◽  
Time Dependent ◽  
Quantum Harmonic Oscillator ◽  
Frequency Dependent ◽  
Fourier Operator ◽  
Time Dependencies ◽  
Dependent Mass

We use the Fourier operator to transform a time-dependent mass quantum harmonic oscillator into a frequency-dependent one. Then we use Lewis–Ermakov invariants to solve the Schrödinger equation by using squeeze operators. Finally, we give two examples of time dependencies: quadratically and hyperbolically growing masses.

scholarly journals Schrödinger equation of a particle in a uniformly accelerated frame and the possibility of a new kind of quanta

2015 ◽  
Vol 30 (38) ◽  
pp. 1550182 ◽  
Author(s):  
Sanchari De ◽  
Sutapa Ghosh ◽  
Somenath Chakrabarty
Keyword(s):  
Exact Solution ◽  
Hydrogen Atom ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Minkowski Spacetime ◽  
Quantum Harmonic Oscillator ◽  
One Dimensional ◽  
Spacetime Geometry

In this paper, we have developed a formalism to obtain the Schrödinger equation for a particle in a frame undergoing a uniform acceleration in an otherwise flat Minkowski spacetime geometry. We have presented an exact solution of the equation and obtained the eigenfunctions and the corresponding eigenvalues. It has been observed that the Schrödinger equation can be reduced to a one-dimensional hydrogen atom problem. Whereas, the quantized energy levels are exactly identical with that of a one-dimensional quantum harmonic oscillator. Hence, considering transitions, we have predicted the existence of a new kind of quanta, which will either be emitted or absorbed if the particles get excited or de-excited, respectively.

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