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Unformatted text preview: order. Compare with the Taylor’s expansions of the exact results. 4. ±ind the Frst nonvanishing corrections to the groundstate energy and wavefunction of the harmonic oscillator when an anharmonic term is added tot he potential. ±irst consider the asymmetric anharmonic oscillator H = P 2 2 M + Mω 2 2 X 2 + λX 3 , then do the same for symmetric anharmonic oscillator H = P 2 2 M + Mω 2 2 X 2 + λX 4 . 5. Consider a 3dimensional Hilbert space spanned by the states  1 A ,  2 A , and  3 A . Let the unperturbed Hamiltonian be H = 16 4 28 4 1 7 28 7 49 . Let the perturbation operator be V = 3 − 5 3 3 − 5 3 . ±ind the eigenvalues of H = H + λV to second order in λ , and Fnd the eigenstates of H to Frstorder....
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This note was uploaded on 11/26/2010 for the course PHYSICS PHYS 852 taught by Professor Michaelmoore during the Spring '10 term at Michigan State University.
 Spring '10
 MichaelMoore
 mechanics, Work

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