A finite difference approach for the calculation of perturbed oscillator energies

A simple numerical method for calculating eigenvalues and corresponding eigenvectors of the Schrodinger equation for a perturbed oscillator is described. The derived results are compared with previously derived numerical data and with available exact values.

[1]  J. Killingbeck.  Direct expectation value calculations , 1985 .

[2]  G. Flessas.  Definite integrals as solutions for the x2+λx2/(1+gx2) potential , 1982 .

[3]  P. K. Srivastava,et al.  Eigenvalues of ?x2m anharmonic oscillators , 1973 .

[4]  J. Killingbeck.  Some applications of perturbation theory to numerical integration methods for the Schrödinger equation , 1979 .

[5]  A. Mitra.  On the interaction of the type λx2/(1+gx2) , 1978 .

[6]  Elise de Doncker,et al.  D01 Chapter-Numerical Algorithms Group, in samenwerking met de andere D01-contributors. 1) NAG Fortran Mini Manual, Mark 8, D01 18p., , 1981 .

[7]  G. Flessas.  On the Schrdinger equation for the x2 + ?x2/(1 + gx2) interaction , 1981 .

[8]  D. Stelman,et al.  Some energy levels and matrix elements of the quartic oscillator , 1963 .

[9]  M. Nagarajan,et al.  Exact solutions of the Schrodinger equation (-d/dx2 + x2 + λx2/(1 + gx2))ψ(x) = Eψ(x) , 1982 .

[10]  J. H. Wilkinson.  The algebraic eigenvalue problem , 1966 .

[11]  J. Killingbeck,et al.  Accurate calculation of perturbed oscillator energies , 1979 .

[12]  N. Bessis,et al.  A note on the Schrödinger equation for the x2+λx2/(1+gx2) potential , 1980 .

[13]  H. D. Vollmer,et al.  The influence of higher order contributions to the correlation function of the intensity fluctuation in a Laser near threshold , 1967 .

[14]  V. S. Varma.  On the x2+λx2/(1+gx2) interaction , 1981 .

[15]  C. S. Lai,et al.  On the Schrodinger equation for the interaction x2+λx2/(1+gx2) , 1982 .