How to fit quantum LHO into quantum mechanics?

[maya :D]

Can anyone help me with this?
The basic equation in quantum mechanics says that E=n*h*v(nu) where n = 1,2,3,...
How is then possible that the quantum linear harmonic oscillator has an energy E=(n+1/2)h*v? If someone can explain this, please help

 

[RedX]

The second equation is correct. If you solve the differential equation for the harmonic oscillator, that's what you get.

If you instead use ladder operators, then maybe you miss out on the 1/2 term, so that's why you got the 1st equation instead. I'm not sure how you are supposed to get the 1/2 term with ladder operators.

 

[Gerenuk]

I'm just guessing that what you mean by the first equation should be some "general QM principle"(?)
$$\Delta E= h\nu$$.

Indeed the second equation is correct for a harmonic oscillator.