(a) Using the potential energy U 1 2m 2 x 2 , develop the Schrdinger equation for the harmonic oscillator (b) Show by substitution that 0 (x) A 0 e a 2x 2 2 satisfies your equation, where 2 m 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 E, (n )ho (35 7)

Question: (a) Using the potential energy U = 1/2m 2 x 2 , develop the Schrdinger equation for the harmonic oscillator. (b) Show by substitution that

(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.

E, = (n + )ho (35.7)

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