ISW hamiltonian in energy basis

  • Thread starter v_pino
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  • #1
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Homework Statement


Find the matrix elements of the Hamiltonian in the energy basis for the ISW. Is it
diagonal? Do you expect it to be diagonal?

Homework Equations



[itex] H=\frac{p^2}{2m}+V [/itex]

[itex] \frac{d}{dt}\langle Q \rangle = \frac{i}{\hbar} \langle[\hat H, \hat Q] \rangle + \langle \frac{\partial \hat Q}{\partial t} \rangle [/itex]


The Attempt at a Solution



How should I convert H into matrix?
 

Answers and Replies

  • #2
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I assume by ISW you mean "infinite square well". Anyway, you're not asked to convert H into a matrix. You are asked to find its matrix elements. Some things: 1) Matrix elements are indexed scalars. 2) "Matrix elements" carries the connotation of "eigenvalues". 3) What happens when the Hamiltonian operator "hits" an energy-basis vector/ket? 4) What is the dual of this equation? Does that get the gears working?
 
  • #3
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Thanks bjnartown, I searched and found this. I already had the correct math down, but your explanation is wonderful and I really learned a lot from it. I seriously created an account to tell you that, lol.
 

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