scholarly journals Comment on ‘Exact solution of the position-dependent effective mass and angular frequency Schrödinger equation: harmonic oscillator model with quantized confinement parameter’

2021 ◽  
Vol 54 (36) ◽  
pp. 368001
Author(s):  
C Quesne
Keyword(s):  
Exact Solution ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Effective Mass ◽  
Schrodinger Equation ◽  
Angular Frequency ◽  
Oscillator Model ◽  
Harmonic Oscillator Model

THE SOLITARY WAVE MODEL OF SUPERFLUIDITY

2005 ◽  
Vol 19 (01n03) ◽  
pp. 99-102 ◽  
Author(s):  
KUANGDING PENG
Keyword(s):  
Exact Solution ◽  
Transition Temperature ◽  
Solitary Wave ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Solitary Waves ◽  
Schrodinger Equation ◽  
Wave Model ◽  
Harmonic Oscillator Model ◽  
Coherent Condition

We propose the solitary wave model of superfluidity. According to harmonic oscillator model of quasi-lattice of liquid, it is proven that superfluid domains (SD) exist in He liquid, in which the resistanceless motion of liquid molecules (LM) can be carry out. At temperature lower than T c, all SD connect with each other and superflow in whole liquid takes place. Applying Toda's potential, under continuous conditions, we obtain the motion equation of LM, and its exact solution. Substituting these results into Schrödinger equation of LM, we can prove the existence of solitary waves of LM and the non-linear Schrödinger equation of LM. The motion of solitons of LM leads to a superflow. On the basis of coherent condition of wave of LM, we derive the formula of transition temperature Tc of superfluidity. From the formula, the relation of the onset temperature Tc of superflow on inert layers is explained.

Lie Algebra Method for Exact Solution of the Schrodinger Equation in One-Dimension with Position-Dependent Effective Mass

2011 ◽  
Author(s):  
Z. Bakhshi ◽  
H. Panahi ◽  
Muhammed Hasan Aslan ◽  
Ahmet Yayuz Oral ◽  
Mehmet Özer ◽  
...  
Keyword(s):  
Exact Solution ◽  
Schrödinger Equation ◽  
Effective Mass ◽  
Lie Algebra ◽  
Schrodinger Equation ◽  
One Dimension ◽  
Algebra Method

scholarly journals COMPLEXIFIER VERSUS FACTORIZATION AND DEFORMATION METHODS FOR GENERATION OF COHERENT STATES OF A 1D NLHO I: MATHEMATICAL CONSTRUCTION

2013 ◽  
Vol 10 (10) ◽  
pp. 1350056 ◽  
Author(s):  
R. ROKNIZADEH ◽  
H. HEYDARI
Keyword(s):  
Exact Solution ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Coherent States ◽  
Schrodinger Equation ◽  
Jacobi Polynomials ◽  
One Dimensional ◽  
The Difference ◽  
Mathematical Construction

Three methods: complexifier, factorization and deformation, for construction of coherent states are presented for one-dimensional nonlinear harmonic oscillator (1D NLHO). Since by exploring the Jacobi polynomials [Formula: see text], bridging the difference between them is possible, we give here also the exact solution of Schrödinger equation of 1D NLHO in terms of Jacobi 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.

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