The Harmonic Oscillator - Thus the harmonic oscillator is...

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The Harmonic Oscillator Now consider a particle subject to a restoring force , as might arise for a mass-spring system obeying Hooke's Law. The potential is then (118) If we choose the energy scale such that then . This potential is also appropriate for describing the interaction of two masses connected by an ideal spring. In this case, we let be the distance between the masses, and for the mass we substitute the reduced mass
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Unformatted text preview: . Thus the harmonic oscillator is the simplest model for the vibrational motion of the atoms in a diatomic molecule, if we consider the two atoms as point masses and the bond between them as a spring. The one-dimensional Schrödinger equation becomes (119) After some effort, the eigenfunctions are (120) where is the Hermite polynomial of degree , and and are defined by (121) The eigenvalues are (122) with ....
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This note was uploaded on 11/22/2011 for the course CHEMISTRY CHM1025 taught by Professor Laurachoudry during the Fall '10 term at Broward College.

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The Harmonic Oscillator - Thus the harmonic oscillator is...

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