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Perturbation theory in quantum mechanics

See attached file.


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I'll explain this in the Dirac notation, see attached pdf file for explanation of this notation.

Let's denote the unperturbed Hamiltonian by H . The eigenstates of H are the states |psi_n>, the corresponding eigenvalues are E_n:

H |psi_n> = E_n |psi_n>

Suppose that we perturb H. The Hamiltonian is now H' = H + X. A convenient way to find the corrections to E_n is to consider instead the Hamiltonian H'(epsilon) = H + epsilon X, work things out order by order in powers of epsilon, and then put epsilon = 1 at the end of the ...

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A detailed explanation is given.