Tunnelling of a large spin: mapping onto a particle problem

Abstract

The tunnelling of a single quantum spin is studied in the limit of large spin quantum number S. The problem is mapped onto a particle problem on the positive half-line with a Hamiltonian which is invariant under inversion x to 1/x. Not only the ground-state energy but also all the other energy levels and corresponding level splittings (if any) are computed by using the conventional WKB methods for the particle problem and an excellent agreement with numerical data is found.