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Unformatted text preview: 3. A particle (of unit mass) trapped by a Dirac delta-function potential (of unit strength) is described by the Hamiltonian H = p 2 2-δ ( 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 Hamil-tonian H = p 2 2 + 1 2 x 2 . [ Note: You might set ~ = 1 to facilitate your numerical calculations.] 4. A one-dimensional harmonic oscillator carrying a charge q is located in an external electric ﬁeld of strength E pointing in the positive x-direction: H =-~ 2 2 m d 2 dx 2 + mω 2 2 x 2-qEx . Calculate the energy levels and wave functions in second-order perturbation theory and compare with the exact results. —— End ——...
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- Spring '11
- mechanics, upper bound, ground state energy, variational ansatz