L12 - Harmonic Oscillator Energy levels of a quantum...

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Classical Harmonic Oscillator
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Amplitude
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Total energy is the sum of kinetic and potential energy Compute kinetic energy K from dx/dt Compute potential energy V from integral of the force: F(x) = -dV(x)/dx Total energy is a constant as a function of time total energy is conserved the system is conservative
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Taylor expansion of potential energy
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Translational motion By introducing relative coordinates, we have reduced a two-body problem to a one body problem
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Quantum Mechanical Harmonic Oscillator
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Lowest eigenvalue Normalize wfs:
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Ground State of Quantum Mechanical
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Unformatted text preview: Harmonic Oscillator Energy levels of a quantum mechanical Harmonic Oscillator The wavefunctions of a harmonic oscillator are given by the product of a Gaussian function and a Hermite polynomial Wavefunctions Probability Densities Energy levels are evenly spaced [ D E does NOT depend on n] –Energy increases linearly with n Properties of the wavefunctions of a harmonic oscillator Vibrational levels of a diatomic molecule Allowed transitions Frequency of absorbed radiation Infrared region for diatomic molecules ~ 10 3 cm -1...
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This note was uploaded on 02/06/2011 for the course CHE 110A taught by Professor Mccurdy during the Fall '09 term at UC Davis.

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L12 - Harmonic Oscillator Energy levels of a quantum...

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