Higher-order semiclassical quantization of an asymmetric double minimum potential

Although the semiclassical quantization condition of a general (asymmetric) double minimum potential has been known for some time it has only been applied to the simpler symmetric case. In this work, new versions of a method for evaluating higher-order semiclassical phase integrals are applied to semiclassical quantization of an asymmetric double minimum potential. The quantization condition is discussed and energy eigenvalues for a model potential are determined in the first- , third- , and fifth-order phase integral approximations. Agreement of three, five, and seven significant digits, respectively, where the exact quantum mechanical eigenenergies are obtained.