Changing the Hamiltonian without affecting the wave function

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SUMMARY

This discussion focuses on methods to change the Hamiltonian in quantum mechanics without altering its wave functions (eigenvectors). Participants suggest multiplying all elements of the Hamiltonian matrix by a constant as a straightforward approach. Additionally, they recommend using canonical transformations or reverting to the Lagrangian formulation to simplify complex Hamiltonians, thereby facilitating easier derivation of wave functions.

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Isaac.Wang88
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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.
 
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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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