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 Hamiltoni-an. Next, find the value of that minimizes the energy, and show that with this choice you re-cover 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
- true ground state, trial function, Nancy Makri