Calculating energy levels of a double-well potential in a two- dimensional system by expanding the potential function around its minimum

Energy eigenvalues are obtained for a double-well potential T E%c+(~ cbc@ ' 3 ~ d % n + on b d % n2 @ % + n + o, in a two-dimensional system, using the Hill- determinant approach, for various values of perturbation parameters ~ cb ,a nd @ .S ome of the results calculated by the Hill-determinant approach are compared with the results produced by other means. R´ esum´ e : Nous calculons les energies propres d'un Hamiltonien 2D qui contient un potentiel a deux minima T E%c+(~ cbc@ ' 3 ~ d % n + on b d % n2 @ % + n + o .N ous utilisons la methode du deterinant de Hill pour diverse valeurs des parametres pertabatifs. Nous comparons certains de ces resultat avec des resultats obtenus d'autres methodes. (Traduit par la r ´

[1]  R. Eid,et al.  Converging bounds for the eigenvalues of multiminima potentials in two-dimensional space , 1996 .

[2]  E. P. Yukalova,et al.  ASYMPTOTIC PROPERTIES OF EIGENVALUES IN VARIATIONAL CALCULATIONS FOR DOUBLE-WELL OSCILLATORS , 1996 .

[3]  M. Witwit.  The energy levels for a symmetric and nonsymmetric double-well potential in a two-dimensional system using the Hill determinant approach , 1996 .

[4]  J. Killingbeck,et al.  A Hill-determinant approach to symmetric double-well potentials in two dimensions , 1995 .

[5]  J. Killingbeck,et al.  Hypervirial perturbation calculations for double-well potentials of perturbed oscillator type , 1993 .

[6]  Handy.  Application of the eigenvalue moment method to the quartic anharmonic double-well oscillator. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[7]  Mamta,et al.  Energy eigenvalues for double-well oscillators with mixed cubic—quartic anharmonicities , 1992 .

[8]  M. Witwit.  Finite difference calculations of eigenvalues for various potentials , 1992 .

[9]  M. Witwit.  The eigenvalues of the Schrodinger equation for spherically symmetric states for various types of potentials in two, three and N dimensions, by using perturbative and non-perturbative methods , 1991 .

[10]  Buenda,et al.  Perturbative-variational calculations in two-well anharmonic oscillators. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[11]  R. Hodgson,et al.  Splitting in a double-minimum potential with almost twofold degenerate lower levels , 1989 .

[12]  H. Meyer,et al.  Some finite difference methods for computing eigenvalues and eigenvectors of special two-point boundary value problems , 1987 .

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

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

[15]  W. E. Caswell.  Accurate energy levels for the anharmonic oscillator and a summable series for the double-well potential in perturbation theory , 1979 .

[16]  K. Banerjee,et al.  Two-well oscillator , 1978 .