Harmonic oscillators

Harmonic oscillators - (9.1) hy is there no linear term?...

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Harmonic oscillators One of the major playing fields for operatorial methods is the harmonic oscillator. Even though they look very artificial, harmonic potentials play an extremely important rôle in many areas of physics. This is due to the fact that around an equilibrium point, where the forces vanish, any potential behaves as an harmonic one (plus small corrections). This can best be seen by making a Taylor series expansion about such a point,
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Unformatted text preview: (9.1) hy is there no linear term? For small enough the quadratic term dominates, and we can ignore other terms. Such situations occur in many physical problems, and make the harmonic oscillator such an important problem. As explained in our first discussion of harmonic oscillators, we scale to dimensionless variables (``pure numbers'') (9.2) In these new variables the Schrdinger equation becomes (9.3)...
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This note was uploaded on 11/09/2011 for the course PHY PHY2053 taught by Professor Davidjudd during the Fall '10 term at Broward College.

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