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Unformatted text preview: Then use Frstorder perturbation theory to compute the energy shift to the ground state of a harmonic oscillator with frequency ω . Here you should use H = P 2 2 M + Mω 2 2 X 2 , and for the perturbation V use your relativistic correction to the kinetic energy. Compute the ratio E (1) /E (0) , and evaluate numerically for an electron, taking the harmonic oscillator length to be the Bohr radius. Do you expect this to be a good estimate of the relativistic correction to the hydrogen atom groundstate energy? 5. A threestate quantum system is described by the Hamiltonian matrix H = 0 0 0 0 1 0 0 0 2 . The system is perturbed by the operator V = 0 1 2 1 0 1 2 1 0 . ±or the Hamiltonian H = H + λV, compute the eigenvalues to third order and the eigenvectors to secondorder. 1...
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This note was uploaded on 10/25/2010 for the course PHYSICS PHYS 851 taught by Professor Michaelmoore during the Fall '08 term at Michigan State University.
 Fall '08
 MichaelMoore
 mechanics, Work

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