(Solution) - For an anharmonic oscillator with a Find E 1 for the state -(2025 Original AI-Free Solution)

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For an anharmonic oscillator with

(a) Find E(1) for the state with quantum number v.
(b) Find E(2) for the state with quantum number v. You will need the following integral (Levine, Molecular Spectroscopy, p. 154):

Where the ((0)'s are harmonic-oscillator wave functions and a is defined by (4.31).
(c) Which unperturbed states contribute to (v(1)?