[SEARCH] [AUTHOR ID] [JOURNAL ID] [RESOURCES] [MSN HOME PAGE] [SEND MAIL] [HELP] [CURR_LIST] Item: 40 of 56 [FIRST_DOC] [PREV_DOC] [NEXT_DOC] [LAST_DOC] ___________ ____ ________ this document in [DVI.......]format. _________________________________________________________________ 80c:65174 65L15 Hautot, André; Magnus, Alphonse Calculation of the eigenvalues of Schrodinger equations by an extension of Hill's method. (English) J. Comput. Appl. Math. 5 (1979), no. 1, 3--15. _________________________________________________________________ Authors' summary: ''The eigenfunctions of the one-dimensional Schrodinger equation Psi ''+(E - V(x)) Psi =0, where V(x) is a polynomial, are represented by expansions of the form {sum}{sub}(k=0){sup}{infin} c{sub}k phi {sub}k(omega , x). The functions phi {sub}k(omega , x) are chosen in such a way that recurrence relations hold for the coefficients c{sub}k: examples treated are D{sub}k(omega x) (Weber-Hermite functions), exp( - omega x {sup}2)x{sup}k and exp( - cx{sup}q)D{sub}k(omega x). From these recurrence relations, one considers an infinite bandmatrix whose finite square sections permit one to solve approximately the original eigenproblem. It is then shown how a good choice of the parameter omega may reduce dramatically the complexity of the computations by a theoretical study of the relation holding between the error on an eigenvalue, the order of the matrix, and the value of omega . The paper contains tables with 10 significant figures of the 30 first eigenvalues corresponding to V(x)=x{sup}(2m), m=2(1)7, and the 6 first eigenvalues corresponding to V(x)=x{sup}2+ lambda x{sup}(10) and x{sup}2+ lambda x{sup}(12), lambda =.01 (.01).1 (.1)1 (1)10 (10)100.'' © Copyright American Mathematical Society 1980, 1995 [CURR_LIST] Item: 40 of 56 [FIRST_DOC] [PREV_DOC] [NEXT_DOC] [LAST_DOC] ___________ ____