**17** **Perturbation theory**

**17.1 Shifting the energy levels**

In physics, it often happens that the problem we wish to solve is close to – but not quite the same as – a problem we actually *can* solve. For example, for motions close to a stable equilibrium point, a classical 1-D particle can usually be regarded as a harmonic oscillator, because the potential function *U*(*x*) is approximately a parabola near its minimum. This fact accounts for the very great importance of the harmonic oscillator in mechanics. The same is true for a quantum particle.^{1} We can solve the classical and quantum harmonic oscillator problems very well by now. Yet most real potential ...

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