scholarly journals Quasi-Exact Solvability of a Hyperbolic Intermolecular Potential Induced by an Effective Mass Step

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Axel Schulze-Halberg
Keyword(s):  
Schrödinger Equation ◽  
Effective Mass ◽  
Explicit Form ◽  
Schrodinger Equation ◽  
Intermolecular Potential ◽  
Third Order ◽  
Exact Solvability ◽  
Exactly Solvable ◽  
Hyperbolic Potential

It is shown that a nonsolvable third-order hyperbolic potential becomes quasi-exactly solvable after the introduction of a hyperbolic effective mass step. Stationary energies andL2-solutions of the corresponding Schrödinger equation are obtained in explicit form.

scholarly journals SUPERSYMMETRIC APPROACH TO EXACTLY SOLVABLE SYSTEMS WITH POSITION-DEPENDENT EFFECTIVE MASSES

2002 ◽  
Vol 17 (31) ◽  
pp. 2057-2066 ◽  
Author(s):  
BEŞİ GÖNÜL ◽  
BÜLENT GÖNÜL ◽  
DİLEK TUTCU ◽  
OKAN ÖZER
Keyword(s):  
Schrödinger Equation ◽  
Effective Mass ◽  
Schrodinger Equation ◽  
Hamiltonian Operator ◽  
One Dimensional ◽  
Exact Solvability ◽  
Exactly Solvable ◽  
The One ◽  
Dependent Mass ◽  
The Relationship

We discuss the relationship between exact solvability of the Schrödinger equation with a position-dependent mass and the ordering ambiguity in the Hamiltonian operator within the framework of supersymmetric quantum mechanics. The one-dimensional Schrödinger equation, derived from the general form of the effective mass Hamiltonian, is solved exactly for a system with exponentially changing mass in the presence of a potential with similar behaviour, and the corresponding supersymmetric partner Hamiltonians are related to the effective-mass Hamiltonians proposed in the literature.

Exactly solvable effective mass Schrödinger equation with coulomb-like potential

2010 ◽  
Vol 110 (15) ◽  
pp. 2880-2885 ◽  
Author(s):  
C. Pacheco-García ◽  
J. García-Ravelo ◽  
J. Morales ◽  
J. J. Peña
Keyword(s):  
Schrödinger Equation ◽  
Effective Mass ◽  
Schrodinger Equation ◽  
Effective Mass Schrödinger Equation ◽  
Exactly Solvable

scholarly journals EXACTLY SOLVABLE EFFECTIVE MASS D-DIMENSIONAL SCHRÖDINGER EQUATION FOR PSEUDOHARMONIC AND MODIFIED KRATZER PROBLEMS

2009 ◽  
Vol 20 (03) ◽  
pp. 361-372 ◽  
Author(s):  
SAMEER M. IKHDAIR ◽  
RAMAZAN SEVER
Keyword(s):  
Schrödinger Equation ◽  
Effective Mass ◽  
Schrodinger Equation ◽  
Arbitrary Dimension ◽  
Bound State ◽  
Exact Bound ◽  
Point Canonical Transformation ◽  
Energy Eigenvalues ◽  
Exactly Solvable ◽  
Molecular Potentials

The point canonical transformation (PCT) approach is used to solve the Schrödinger equation for an arbitrary dimension D with a power-law position-dependent effective mass (PDEM) distribution function for the pseudoharmonic and modified Kratzer (Mie-type) diatomic molecular potentials. In mapping the transformed exactly solvable D-dimensional (D ≥ 2) Schrödinger equation with constant mass into the effective mass equation by using a proper transformation, the exact bound state solutions including the energy eigenvalues and corresponding wave functions are derived. The well-known pseudoharmonic and modified Kratzer exact eigenstates of various dimensionality is manifested.

scholarly journals On the position-dependent mass Schrödinger equation for Mie-type potentials

2021 ◽  
Vol 2090 (1) ◽  
pp. 012165
Author(s):  
G Ovando ◽  
J J Peña ◽  
J Morales ◽  
J López-Bonilla
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Energy Operator ◽  
Constant Mass ◽  
Point Canonical Transformation ◽  
Mass Distributions ◽  
Exactly Solvable ◽  
Reference Problem ◽  
Dependent Mass ◽  
Position Dependent Mass

Abstract The exactly solvable Position Dependent Mass Schrödinger Equation (PDMSE) for Mie-type potentials is presented. To that, by means of a point canonical transformation the exactly solvable constant mass Schrödinger equation is transformed into a PDMSE. The mapping between both Schrödinger equations lets obtain the energy spectra and wave functions for the potential under study. This happens for any selection of the O von Roos ambiguity parameters involved in the kinetic energy operator. The exactly solvable multiparameter exponential-type potential for the constant mass Schrödinger equation constitutes the reference problem allowing to solve the PDMSE for Mie potentials and mass functions of the form given by m(x) = skx s-1/(xs + 1))2. Thereby, as a useful application of our proposal, the particular Lennard-Jones potential is presented as an example of Mie potential by considering the mass distribution m(x) = 6kx 5/(x 6 + 1))2. The proposed method is general and can be straightforwardly applied to the solution of the PDMSE for other potential models and/or with different position-dependent mass distributions.

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