hw5 - Chemistry 550 / 475 Homework Assignment #5 due:...

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Chemistry 550 / 475 – Homework Assignment #5 due: Friday, October 28th at 5:00 pm Readings : Chapters 4 and 5 in Levine Problem 1 - Eigenfunctions of the harmonic oscillator. For the one-dimensional linear harmonic oscillator the potential energy term in the Schr¨odinger equation is V ( x ) = 1 2 2 x 2 . Since the harmonic oscillator Hamiltonian corresponds to the observable energy of the os- cillator we know, inter alia, that its eigenfunctions ψ n ( x ) = C n H n ± r ~ x ² e - mωx 2 / 2 ~ must be orthogonal and, further, can be engineered to be orthonormal. a. Find the appropriate coefficients C n that ensure the orthonormality of the harmonic oscillator eigenfunctions ψ n . The functions H n ( z ) = ( - ) n e z 2 ( d n /dz n ) e - z 2 are known as the Hermite polynomials of order n . Verify the eigenfunction’s orthonormality by computing h ψ n | ψ m i ≡ h n | m i . b. Using your favorite plotting tool plot the lowest five (5) states of the harmonic oscillator. c.
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This note was uploaded on 01/18/2012 for the course CHEM 550/475 taught by Professor Davidj.masiello during the Fall '11 term at University of Washington.

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hw5 - Chemistry 550 / 475 Homework Assignment #5 due:...

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