Calculation of oscillator (Talmi–Moshinsky–Smirnov) brackets

Published: 10-05-2021| Version 1 | DOI: 10.17632/4m594wzv94.1
Victor D. Efros


A program to calculate the oscillator brackets, or Talmi–Moshinsky–Smirnov coefficients, is presented. The recursion with respect to radial quantum numbers is employed. The listed runs show that the program is very fast and it produces accurate results up to very high oscillator excitations. The amount of computations per bracket does not increase with the increase of quantum numbers. In one of the presented versions, the program provides the sets of all existing brackets of a given parity pertaining to oscillator excitations and total angular momenta which lie within given ranges. In the other version, the subsets of such brackets having given angular momenta are produced. Such type arrays of the brackets are quite convenient for majority of applications. These arrays are made compact due to use of suitable combinations of partial angular momenta as array arguments. The program is easy to implement and follow. Comparisons are made with results of programs based on the explicit expression for the brackets.