Computing the coefficients of transformations between oscillator states

TL;DR

This paper introduces a fast, accurate recursive program for computing Moshinsky brackets, enabling efficient calculations of oscillator state transformations with high precision for large quantum numbers.

Contribution

A new recursive algorithm and program for rapid, precise computation of Moshinsky brackets in quantum oscillator state transformations.

Findings

Computing time per bracket is approximately 10^{-8} seconds.

High accuracy maintained for quantum numbers up to 80.

Program is user-friendly and suitable for single-processor notebooks.

Abstract

A program is created to compute recursively the Moshinsky brackets. It is very fast and provides highly accurate results. In the case of the double-precision computations with a single-processor consumer notebook, the computing time per bracket at any not small oscillator excitations is on the scale of 10^{-8} s and the accuracy is very good for the total number of quanta up to 80. The program is easy to handle.