Remarks on the solution of the position-dependent mass Schrödinger equation (original) (raw)

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.

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.

Remarks on the Solution of the Position Dependent Mass (PDM)

arXiv (Cornell University), 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.

Analytical solution to position dependent mass Schrödinger equation

Journal of Modern Optics, 2011

Using a recently developed technique to solve Schrödinger equation for constant mass, we studied the regime in which mass varies with position i.e position dependent mass Schrödinger equation(PDMSE). We obtained an analytical solution for the PDMSE and applied our approach to study a position dependent mass m(x) particle scattered by a potential V(x). We also studied the structural analogy between PDMSE and two-level atomic system interacting with a classical field. PACS numbers: 03.65.Ge; 03.65.Fd; 03.65.-w Schrödinger equation with position dependent mass is one of the areas of research which has gained great attention in the past decades. Position-dependent mass Schrödinger equation(PDMSE) has been applied to several physical systems. For example PDMSE is applied in electronic properties of semiconductors [1], quantum dots and quantum wells [2, 3], semiconductors heterostructures [4], supper-lattice band structures [5], He-Clusters [6] quantum liquids [7], the dependence of energy gap on magnetic field in semiconductor nano-scale rings [8], the solid state problem with Dirac equation [9]

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.

A New Approach to the Exact Solutions of the Effective Mass Schr�dinger Equation

Int J Theor Phys, 2008

The Schrodinger equation is solved exactly for some well known potentials. Solutions are obtained reducing the Schrodinger 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.

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.

Analytic results in the position-dependent mass Schrodinger problem

Communications in Theoretical Physics

We investigate the Schrodinger equation for a particle with a nonuniform solitonic mass density. First, we discuss in extent the (nontrivial) position-dependent mass V (x) = 0 case whose solutions are hypergeometric functions in tanh 2 x. Then, we consider an external hyperbolic-tangent potential. We show that the effective quantum mechanical problem is given by a Heun class equation and find analytically an eigenbasis for the space of solutions. We also compute the eigenstates for a potential of the form V (x) = V0 sinh 2 x. *