Chapter 35, Problem 59P

(a)

To determine

Schrödinger equation for the harmonic oscillator if the potential energy is $U=m{\omega }^2{x}^2/2$.

(b)

To determine

To show: The substitution ${\psi }_0\left(x\right)=A_0{e}^{-{\alpha }^2{x}^2/2}$ satisfies the Schrödinger equation and the energy is given by equation 35.7 with $n=0$.

(c)

To determine

The normalization constant for given ground state wave function.