Quasiclassical wave function in multidimensional quantum decay problems

Abstract

The quantum decay rate of metastable state is calculated in quasiclassical accuracy. Specifically, the calculation is based entirely on the standard quasiclassical ansatz, where the wave function is put equal to exp-(action)/ħ, and where the action is expanded in powers of ħ. Such a calculation is well known in the case of one-dimensional systems, and not so well known for multidimensional systems. Therefore, this paper intends to give a comprehensive presentation of the quasiclassical method. A straightforward procedure leads to a decay rate which agrees with the one obtained by the instanton technique. However, a calculation of the entire wave function shows that the procedure is consistent only if the metastable state is dominated by an internal degree of freedom which is slow in comparison with the remaining degrees of freedom.