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Changing the Hamiltonian without affecting the wave function

  1. Mar 9, 2014 #1
    How many ways can we change the Hamiltonian without affecting the wave functions (eigenvectors) of it.
    Like multiply all the elements in the matrix by a constant.
    I'm facing a very difficult Hamiltonian,:cry: I want to simplify it, so the wave function will be much easier to derive.
    Thanks in advance.
     
  2. jcsd
  3. Mar 9, 2014 #2

    UltrafastPED

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    Science Advisor
    Gold Member

    Try Canonical transformations.

    Or revert to the Lagrangian and work it over - much more freedom there - then convert it back. This is equivalent to the canonical transformations.
     
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