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Matrix elements for the modified Pöschl—Teller potential
Author(s) -
Zúñiga José,
Alacid Mercedes,
Requena Alberto,
Bastida Adolfo
Publication year - 1996
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/(sici)1097-461x(1996)57:1<43::aid-qua5>3.0.co;2-z
Subject(s) - eigenfunction , matrix (chemical analysis) , recursion (computer science) , hyperbolic function , computation , factorization , wave function , algebra over a field , pure mathematics , physics , mathematics , quantum mechanics , mathematical analysis , eigenvalues and eigenvectors , chemistry , algorithm , chromatography
Analytical exact expressions are obtained for matrix elements of the modified Pöschl‐Teller oscillator over different operators including powers of the hyperbolic functions sinh(α x ), cosh(α x ), and tanh(α x ) and the differential operators d / dx and d 2 / dx 2 . These expressions are derived using explicitly the Pöschl‐Teller eigenfunctions. In addition, several recursion relations connecting different Pöschl‐Teller matrix elements are obtained using the factorization and hypervirial techniques. It is shown that these relations can be used to make easier the computation of the matrix elements. © 1996 John Wiley & Sons, Inc.