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A theory of shift operators with applications to nonharmonic systems
Author(s) -
Burrows B. L.,
Cohen M.,
Feldmann T.
Publication year - 2001
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/qua.1103
Subject(s) - hamiltonian (control theory) , hermitian matrix , constructive , hypergeometric function , mathematics , quantum , operator theory , algebra over a field , class (philosophy) , mathematical physics , pure mathematics , quantum mechanics , physics , computer science , mathematical optimization , process (computing) , operating system , artificial intelligence
We present a theory of shift operators (i.e., operators which shift given solutions into other solutions), including their relationship with deformed algebras and describe a general constructive method which enables us to calculate such operators for a wide class of problems. These include the classical linear differential equations of the hypergeometric and confluent hypergeometric functions, a number of soluble nonrelativistic Schrödinger equations (including one with a non‐Hermitian Hamiltonian), and a simple master equation. In general, the resulting shift‐up and shift‐down operators are level dependent but allow for the sequential generation of all required solutions. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001