WKB and MAF quantisation rules for spatially confined quantum mechanical systems

A formalism is developed to obtain the energy eigenvalues of spatially confined quantum mechanical systems in the framework of the usual Wentzel-Kramers-Brillouin (WKB) and Modified Airy Function (MAF) methods. To illustrate the working rule, the techniques are applied to 3 different cases, viz. the confined 1-dimensional harmonic and quartic oscillators, and a boxed-in charged particle subject to an external electric field. The energies thus obtained are compared with those from shifted 1/N expansion, variational and other methods, as well as the available exact numerical results. e-mail:res9523 @ www.isical.ac.in e-mail:raj @ www.isical.ac.in