Harmonic Oscillator Consider a system with a potential ener

Harmonic Oscillator * Consider a system with a potential energy function given by V(x) = 1/2mw^2x^2 What is the energy of the ground state? What is the energy of the first excited state? What is the energy of the nth excited state? Give a brief explanation for your responses (just one or two sentences).

Solution

1. Ground energy level of a harmonic osscilator
E0 = ( 1/2)h w/2pi

2. First excited energy level of a harmonic osscilator
E1 = (3/2)h w/2pi

3. nth energy level of a harmonic osscilator
En = (n + 1/2)h w/2pi