Trajectories in the complex phase space and quantization by numerical contour integration

In this paper an exact numerical quantization method, based on quantum action variable theory is presented. The quantum momentum function (QMF) is redefined such that the corresponding quantum action variable (QAV) is an integer (1=h) for energy eigenvalues and non integer for off eigenvalues. The energy eigenvalues obtained by quantizing the quantum action variable are exact up to the accuracy of the numerical methods used. One of the major advantages of this method is that one could use interpolations or extrapolations for obtaining boundstate energies from a set of QAV values corresponding to non-eigen energies. Examples are given to illustrate the new numerical method and the interpolation and extrapolation methods.

doi:10.4038/sljp.v1i0.167

Sri Lankan Journal of Physics, Vol.1,(2000) 23-31