A Theory of Shift Operators with Applications to Nonharmonic Systems

摘要

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 classicla linear differential equations of the hypergeometric and confluent hypergeometic funtions , a number of soluble nonrelativistic Schrodinger 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 out level dependent but allow for the sequential generation of all required solutions