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Composite Systems - QM

  • Thread starter bon
  • Start date
  • #1
bon
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Homework Statement



Please see attached problem


Homework Equations





The Attempt at a Solution



Ok so im just stuck on the bit that asks us to write down the appropriate form of the interaction hamiltonian H int for two oscillating particles connected by a weak spring. Is it 1/2 k (xa - xb) ^2?

It asks whether HA commutes with Hint. Not sure about this>? What would be the physical significance?
 

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Answers and Replies

  • #2
195
1
H_A contains a derivative. H_int contains a polynomial.
Do you think they can commute? You can work it out.

If H_A and H_int commute, and that the total hamiltonian is their sum, you can find common eigenstates between H_A and H_int.
Else, no, you'll have to solve the complete hamiltonian.
 
  • #3
bon
559
0
Is my expression for H_int correct?

I guess they don't commute then?
 
  • #4
195
1
yes.

yes.
 

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