- #1

broegger

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Hi,

I'm new to this subject, so bear with me. We consider the harmonic oscillator with a pertubation:

(What kind of a perturbation is that anyway, it's not a disturbance in the potential, what does it correspond to physically.)

Now I have to calculate the first and second order energy corrections. I express p by the ladder operators:

I find that the first order correction is 0, and that the second order correction is [tex]E_n^2=m\alpha^2/2[/tex], that is, the energy shift is INDEPENDENT of n (i.e. it is the same for all excited states of the oscillator), but this can't be true, can it?

I'm new to this subject, so bear with me. We consider the harmonic oscillator with a pertubation:

[tex]\hat{H}' = \alpha\hat{p}.[/tex]

(What kind of a perturbation is that anyway, it's not a disturbance in the potential, what does it correspond to physically.)

Now I have to calculate the first and second order energy corrections. I express p by the ladder operators:

[tex]p=i\sqrt{\tfrac{\hslash m\omega}2}(a_+-a_-).[/tex]

I find that the first order correction is 0, and that the second order correction is [tex]E_n^2=m\alpha^2/2[/tex], that is, the energy shift is INDEPENDENT of n (i.e. it is the same for all excited states of the oscillator), but this can't be true, can it?

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