Uniform semiclassical approximation to supersymmetric quantum mechanics

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Abstract
Recently, A. Comtet, A. D. Bandrauk, and D. K. Campbell [Phys. Lett. 150, 159 (1985)] introduced a modified semiclassical quantization rule motivated by the structure of supersymmetric quantum mechanics. In this paper, following their modified semiclassical framework, we provide a method to obtain wave functions in a uniform approximation. We demonstrate our method by constructing wave functions for the Morse, Rosen-Morse, and anharmonic oscillator potentials. Accurate fits to the wave functions are found for all three potentials.