PS6-08 - Chem 442 Homework Set#6 DUE Wednesday 1 2 3 McQ&S...

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Chem 442 Homework Set #6 DUE: Wednesday, November 12, 2008 1) McQ&S 6-46 2) McQ&S 6-47 3) In this problem and the next, we will find the approximate solutions for the quartic oscillator using the variational method. The Hamiltonian for the quartic oscillator is given by: 22 4 2 ˆ 2 d HD mdx =− + = x In this problem, use the ground state wavefunction of the harmonic oscillator (use 2 , not β α ) as the trial function. You can then treat as a variational parameter. Note: the integral covers x −∞≤ ≤∞ . a) Show that the optimal value for the variational parameter is 1/6 2 6 opt Dm ⎛⎞ = ⎜⎟ ⎝⎠ = . b)
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This note was uploaded on 02/12/2011 for the course CHEMISTRY 442 taught by Professor Lizzy during the Spring '10 term at Hanoi University of Technology.

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