1d potential and switching between operators

[Brewer]

Homework Statement

Homework Equations

The Attempt at a Solution

As a group we're stuck on this as a result of the lecturer saying that he wouldn't help us because we should work as a group and find other ways other than asking him about it. Which is fair enough - but none of us understand what's going on!

So far I have tried substituting in for p in the middle of the bracket with -ihd/dx and then used the commutation relationship to try substituting ih for xp - px, but this seems to leave me being nowhere.

I also tried starting with the bracket having H in the middle and substituting for that - this kind of left me with a bracket with p in the middle and one with x in the middle, but whilst this kind of left things in a format that almost looked correct the two brackets were not equal to one another, only additive.

Could anyone suggest a starting point to look at or just any other helpful information that I may have missed when rereading my notes.

 

[borgwal]

Well, have you calculated [x,H]?

Then you can calculate <n|[x,H]|n'> in two different ways: equating the two answers gives you the desired result.

 

[Brewer]

No I hadn't - I thought that was to do with the second part of the question.

I shall give that a go now!