(a) Using the potential energy U = 1/2m 2 x 2 , develop the Schrdinger equation for...

(a) Using the potential energy U = 1/2mω²x², develop the Schrödinger equation for the harmonic oscillator.
(b) Show by substitution that ψ₀(x) = A₀e^{-a^2x^2/2} satisfies your equation, where α² = mω/ℏ and the energy is given by Equation 35.7 with n = 0. (c) Find the normalization constant A0. You then have the ground-state wave function for the harmonic oscillator.

Transcribed Image Text:

E, = (n + )ho (35.7)