First-order correction

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1. Calculate the first-order correction to [tex]E^{3}_{(0)}[/tex] for a particle in a one-dimensional box with walls at x = 0 and x = a due to the following perturbations:

(a) H' = [tex]10^{-3}[/tex][tex]E_{1}[/tex]x/a
(b) H' = [tex]10^{-3}[/tex][tex]E_{1}[/tex]sin(x/a)

The Attempt at a Solution



The only attempt that I have made is to start with the equation [tex]E_{n}[/tex]=[tex]E^{(0)}_{n}[/tex]+[tex]H'_{nn}[/tex]. But I have not really gotten anywhere with it. Does anyone have any ideas where to start with this question?

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The Attempt at a Solution

 
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  • #2
vela
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The first-order correction to the energy of state [itex]|n\rangle[/itex] is H'nn, which is the matrix element [itex]\langle n|H'|n \rangle[/itex]. You just need to calculate that for the given state and perturbations.
 
  • #3
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The first-order correction to the energy of state [itex]|n\rangle[/itex] is H'nn, which is the matrix element [itex]\langle n|H'|n \rangle[/itex]. You just need to calculate that for the given state and perturbations.

That is actually very helpful, thank you so much!!
 

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