For the harmonic oscillator potential energy U =½kx2, the ground-state wave function is  a...

For the harmonic oscillator potential energy U =½kx2, the ground-state wave function is  and its energy is  

(a) Find the classical turning points for a particle with this energy.

(b) The Schrödinger equation says that ψ(x) and its second derivative should be of the opposite sign when E > U and of the same sign when E< U. These two regions are divided by the classical turning points. Verify the relationship between ψ(x) and its second derivative for the ground-state oscillator wave function. (Hint: Look for the inflection points.)