Interpreting the Harmonic Oscillator

[actionintegral]

Ok - here goes:

I see the energy levels of the harmonic oscillator as

E = hw(n+1/2) = hwn + hw/2 (please ignore the lack of cool symbols)

Now the hw/2 is something called the ground state - fine - no problem.

Should I interpret homework as the fundamental harmonic?
2hw as the second harmonic? nhw as the nth harmonic?

etc? etc? Does this mean that the frequency of the harmonic oscillator is
increasing as n increases?

 

[StatMechGuy]

It's just the energy spectrum of the system. It's the same as interpretting the energy spectrum for any other bound state system.

The real interest in the harmonic oscillator comes from using the algebra to deal with second quantization.

 

[Haelfix]

Well I wouldn't quite say that (although the harmonic oscillator is of course very important in making progress with field theory). The main physical interest of the harmonic oscillator imo is quite classical. Namely, the fact that any stable physical system will always have a Fourier decomposition along small perturbations away from a saddle point, so in large part it suffices to say that physics is the study of many harmonic oscillator like systems.