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Perturbation Theory

  1. Mar 8, 2005 #1
    I have been studying Perturbation theory in my Quantum class but my professor has not really explained why physically it comes into play. The book says that perturbation theory is used to help come up with approximate solutions to the Schrodinger Equation. Is this analagous to how we use Fourier series to express solutions to partial differential equations as infinite series? Only instead of using an infinite number of terms, we take the first few for an approximation ? Is there any physical significance or is perturbation theory just pure mathematics?
  2. jcsd
  3. Mar 8, 2005 #2


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    The reason physicists use perurbation theory is that they CAN'T DO the full non-perturbative theory - can't derive and solve the equations. Non-perturbative means with the full strength of the interactions included. So they start with a free theory - no interactions at all, and add just a tiny interaction, called a perturbation, and expand solutions for this in terms of a power series in the coupling constant. If the constant is small, like alpha ~ 1/137, the series will converge, or at least be asymptotic (good results out to some hopefully high power, where it blows up). Perturbation is an approximation technique and should not be compared to Fourier analysis which is a theoretically exact technique (though of course it has its own approximation schemes!).
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