Calculation of eigenvalues through recurrence relations

A simple, fast, and accurate method is developed to calculate eigenvalues when the secular equation can be written as a (2m+1)‐term recurrence relation. Several physically interesting examples are discussed to show that the present algorithm compares favorably with the most efficient ones.

[1]  C. Gerry Nonperturbative dynamical-group approach to the charmonium potential , 1986 .

[2]  J. Killingbeck Hill determinants and 1/N theory , 1985 .

[3]  D. Stanzial,et al.  Improved calculations for anharmonic oscillators using the gradient method , 1985 .

[4]  M. Znojil,et al.  The anharmonic oscillator problem: a new algebraic solution , 1985 .

[5]  E. Castro,et al.  Energy eigenvalues from a modified operator method , 1985 .

[6]  E. Castro,et al.  A simple iterative solution of the Schrodinger equation in matrix representation form , 1985 .

[7]  Chaudhuri Rn Comment on the anharmonic oscillator and the analytic theory of continued fractions. , 1985 .

[8]  Miller,et al.  Comment on "Simple procedure to calculate accurate energy levels of a double-well anharmonic oscillator" , 1985, Physical review. D, Particles and fields.

[9]  E. Castro,et al.  Convergence radii of the Rayleigh-Schrödinger perturbation series for a diatomic rigid polar molecule in a uniform electric field , 1985 .

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

[11]  G. Arteca,et al.  Summation of strongly divergent perturbation series , 1984 .

[12]  M. Znojil Schrodinger equation as recurrences. II. General solutions and their physical asymptotics , 1984 .

[13]  B. Burrows,et al.  A variational-iterative technique applied to quantum mechanical problems , 1984 .

[14]  A. F. Pacheco,et al.  Simple procedure to compute accurate energy levels of a double-well anharmonic oscillator , 1983 .

[15]  A. Hautot,et al.  On the applicability of the Hill determinant method , 1983 .

[16]  W. K. Burton,et al.  On the moment problem for non-positive distributions , 1982 .

[17]  B. Harms,et al.  A method for numerical determination of eigenvalues , 1982 .

[18]  K. Banerjee,et al.  The anharmonic oscillator , 1978, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

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

[20]  C. E. Reid Energy eigenvalues and matrix elements for the quartic oscillator , 1970 .

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