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Unformatted text preview: 3. A particle (of unit mass) trapped by a Dirac deltafunction potential (of unit strength) is described by the Hamiltonian H = p 2 2δ ( x ) . Apply the linear variational theory to determine its ground state energy using the basis of eigenfunctions of the simple harmonic oscillator described by the Hamiltonian H = p 2 2 + 1 2 x 2 . [ Note: You might set ~ = 1 to facilitate your numerical calculations.] 4. A onedimensional harmonic oscillator carrying a charge q is located in an external electric ﬁeld of strength E pointing in the positive xdirection: H =~ 2 2 m d 2 dx 2 + mω 2 2 x 2qEx . Calculate the energy levels and wave functions in secondorder perturbation theory and compare with the exact results. —— End ——...
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This note was uploaded on 12/10/2011 for the course PHYS 4221 taught by Professor Cflo during the Spring '11 term at CUHK.
 Spring '11
 CFLO
 mechanics

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