Energy levels of a harmonic oscillator

 

Remember that for a harmonic oscillator, solving the Schrödinger equation gives energy levels

Ev=(v+1/2)hn         v=0, 1, 2…..   (1)

 

This shows that an oscillator like this cannot be at rest - the minimum vibrational energy it can have is hn/2 - the zero-point energy. 

 

The frequency, n, is related to the force constant, k, for the vibration:

                              (2)

 

The force constant, k, is given by the second derivative of the potential energy, which in one dimension is k=(d2V/dx2). 

 

Next: polyatomic molecules and mass weighting