Unformatted text preview: As an illustration, find the expectation value of a harmonic oscillator Hamiltonian with a trial function of the type 2 ( ) x x cxe Î»Î¨ = . Show that this trial function is orthogonal to the true ground state wavefunction of this Hamiltonian. Next, find the value of that minimizes the energy, and show that with this choice you recover the exact energy of the first excited state. This happens here because the trial function hap pens to have the same form as the exact wavefunction....
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 Fall '08
 Mccall
 true ground state, trial function, Nancy Makri

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