(a) Show by direct substitution in the Schrdinger equation

Chapter 40, Problem 40.58

(choose chapter or problem)

(a) Show by direct substitution in the Schrdinger equation for the one-dimensional harmonic oscillator that the wave function c11x2 = A1xe-a2 x2>2 , where a2 = mv>U, is a solution with energy corresponding to n = 1 in Eq. (40.46). (b) Find the normalization constant A1. (c) Show that the probability density has a minimum at x = 0 and maxima at x = {1>a, corresponding to the classical turning points for the ground state n = 0

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