Problem+Set+3

Problem+Set+3 - constant 1 a Show that is normalized b Show...

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Chemistry 120A, Fall 2008 Problem Set 3 Revised Due Friday, September 19, 2008 New Problems A model system that we have not yet looked at is the harmonic oscillator. This can be used as a model for the vibrations of a diatomic molecule. The first few eigenfunctions (those corresponding to the lowest energy eigenvalues) are given by (Page 170 of McQuarrie and Simon): ! 0 = " # $ % 1 4 e ( x 2 2 1 x ( ) = 4 3 $ % ) * 1 4 xe ( x 2 2 2 x ( ) = 4 $ % 1 4 2 x 2 ( 1 ( ) e ( x 2 2 where is a constant equal to = k μ ( ) 1 2 h . is a parameter related to the mass of the molecule known as the reduced mass, and k is related to how tightly the atoms are held together (it s classical analogue it would be a spring
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Unformatted text preview: constant). 1. a) Show that is normalized b) Show that 1 and 2 are orthogonal The Hamiltonian for a harmonic oscillator is given by ˆ H = ! h 2 2 d 2 dx 2 + 1 2 kx 2 2. a) What do the terms in the Hamiltonian represent? What is the form of the potential energy? b) Calculate the energies corresponding to , 1 and 2 using the time independent Schrödinger equation (your answer can be in terms of the constants , , and h ). Do you notice any patterns? Problems from McQuarrie and Simon Chapter 3 28 and 34 Chapter 4 16 and 32...
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This note was uploaded on 09/28/2009 for the course CHEM 120A taught by Professor Whaley during the Spring '07 term at Berkeley.

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