A New Approach to the Exact Solutions of the Effective Mass Schr�dinger Equation (original) (raw)
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Remarks on the solution of the position-dependent mass Schrödinger equation
Journal of Physics A: Mathematical and Theoretical, 2010
An approximate method is proposed to solve position dependent mass Schrödinger equation. The procedure suggested here leads to the solution of the PDM Schrödinger equation without transforming the potential function to the mass space or vice verse. The method based on asymptotic Taylor expansion of the function, produces an approximate analytical expression for eigenfunction and numerical results for eigenvalues of the PDM Schrödinger equation. The results show that PDM and constant mass Schrödinger equations are not isospectral. The calculations are carried out with the aid of a computer system of symbolic or numerical calculation by constructing a simple algorithm.
Modern Physics Letters A, 2004
A systematic procedure to study one-dimensional Schrödinger equation with a position-dependent effective mass (PDEM) in the kinetic energy operator is explored. The conventional free-particle problem reveals a new and interesting situation in that, in the presence of a mass background, formation of bound states is signalled. We also discuss coordinate-transformed, constant-mass Schrödinger equation, its matching with the PDEM form and the consequent decoupling of the ambiguity parameters. This provides a unified approach to many exact results known in the literature, as well as to a lot of new ones.
Exact Solution of Effective Mass Schrödinger Equation for the Hulthen Potential
International Journal of Theoretical Physics, 2008
A general form of the effective mass Schrödinger equation is solved exactly for Hulthen potential. Nikiforov-Uvarov method is used to obtain energy eigenvalues and the corresponding wave functions. A free parameter is used in the transformation of the wave function.
A General Approach for the Exact Solution of the Schrödinger Equation
International Journal of Theoretical Physics, 2009
The Schrödinger equation is solved exactly for some well known potentials. Solutions are obtained reducing the Schrödinger equation into a second order differential equation by using an appropriate coordinate transformation. The Nikiforov-Uvarov method is used in the calculations to get energy eigenvalues and the corresponding wave functions.
A systematic study on the exact solution of the position dependent mass Schr dinger equation
Journal of Physics A: Mathematical and General, 2003
An algebraic method of constructing potentials for which the Schrödinger equation with position dependent mass can be solved exactly is presented. A general form of the generators of su(1,1) algebra has been employed with a unified approach to the problem. Our systematic approach reproduces a number of earlier results and also leads to some novelties. We show that the solutions of the Schrödinger equation with position dependent mass are free from the choice of parameters for position dependent mass. Two classes of potentials are constructed that include almost all exactly solvable potentials.
Remarks on the Solution of the Position Dependent Mass (PDM) Schr\" odinger Equation
An approximate method is proposed to solve position dependent mass Schrödinger equation. The procedure suggested here leads to the solution of the PDM Schrödinger equation without transforming the potential function to the mass space or vice verse. The method based on asymptotic Taylor expansion of the function, produces an approximate analytical expression for eigenfunction and numerical results for eigenvalues of the PDM Schrödinger equation. The results show that PDM and constant mass Schrödinger equations are not isospectral. The calculations are carried out with the aid of a computer system of symbolic or numerical calculation by constructing a simple algorithm.
Exact solutions of the position-dependent-effective mass Schrödinger equation
The position-dependent effective mass Schrödinger equation exhibiting a similar position dependence for both the potential and mass is exactly solved. Some physical examples are given for bound and scattering systems. We analyze the behavior of the wavefunctions for scattered states in light of the parameters involved. We show that the parameters of the potential play a crucial role.
Exact Solutions of Effective-Mass Schrödinger Equations
Modern Physics Letters A, 2002
We outline a general method for obtaining exact solutions of Schrödinger equations with a position-dependent effective mass and compare the results with those obtained within the frame of supersymmetric quantum theory. We observe that the distinct effective mass Hamiltonians proposed in the literature in fact describe exactly equivalent systems having identical spectra and wave functions as far as exact solvability is concerned. This observation clarifies the Hamiltonian dependence of the band-offset ratio for quantum wells.
0 Remarks on the Solution of the Position Dependent Mass (PDM) Schrödinger Equation
2010
An approximate method is proposed to solve position dependent mass Schrödinger equation. The procedure suggested here leads to the solution of the PDM Schrödinger equation without transforming the potential function to the mass space or vice verse. The method based on asymptotic Taylor expansion of the function, produces an approximate analytical expression for eigenfunction and numerical results for eigenvalues of the PDM Schrödinger equation. The results show that PDM and constant mass Schrödinger equations are not isospectral. The calculations are carried out with the aid of a computer system of symbolic or numerical calculation by constructing a simple algorithm.