An approximate method is proposed to solve the position-dependent mass (PDM) 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 versa. The method based on the 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 the 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.An approximate method is proposed to solve the position-dependent mass (PDM) 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 versa. The method based on the 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 the 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.

arXiv:1009.0250Journal of Physics A Mathematical and TheoreticalOct 19, 201018 citations

Variational Gaussian approximation for the magnetic Schrödinger equation

Selina Burkhard, Benjamin Dörich, Marlis Hochbruck +1 more

In the present paper we consider the semiclassical magnetic Schrödinger equation, which describes the dynamics of particles under the influence of a magnetic field. The solution of the Schrödinger equation is approximated by Gaussian wave packets via the time-dependent variational formulation by Dirac and Frenkel. For the numerical approximation we derive ordinary differential equations for the parameters of the variational solution. Moreover, we prove $L^2$ -error bounds and observable error bounds for the approximating Gaussian wave packet.In the present paper we consider the semiclassical magnetic Schrödinger equation, which describes the dynamics of particles under the influence of a magnetic field. The solution of the Schrödinger equation is approximated by Gaussian wave packets via the time-dependent variational formulation by Dirac and Frenkel. For the numerical approximation we derive ordinary differential equations for the parameters of the variational solution. Moreover, we prove $L^2$-error bounds and observable error bounds for the approximating Gaussian wave packet.

arXiv:2310.16734Jan 1, 20230 citations

Numerical Solution of the Schrödinger Equation

Elsevier eBooksJan 1, 19954 citations

A New Approximation Method for the Schrödinger Equation

F.-Z. Ighezou, R.J. Lombard

Annals of PhysicsDec 1, 199917 citations

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

Ramazan Koç, Seda Sayõn

An approximate method is proposed to solve position dependent mass Schrodinger equation. The procedure suggested here leads to the solution of the PDM Schrodinger equation without trans- forming 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 Schrodinger equation. The results show that PDM and constant mass Schrodinger 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.An approximate method is proposed to solve position dependent mass Schrodinger equation. The procedure suggested here leads to the solution of the PDM Schrodinger equation without trans- forming 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 Schrodinger equation. The results show that PDM and constant mass Schrodinger 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.

Jan 1, 20100 citations

L^2

-error bounds and observable error bounds for the approximating Gaussian wave packet.