
3.2: Implicit Boundary Conditions

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In many physical problems we have implicit boundary conditions, which just mean that we have certain conditions we wish to be satisfied. This is usually the case for systems deﬁned on an inﬁnite deﬁnition area. For the case of the Schrödinger equation this usually means that we require the wavefunction to be normalizable. We thus have to disallow the wave function blowing up at inﬁnity. Sometimes we implicitly assume continuity or diﬀerentiability. In general one should be careful about such implicit BC’s, which may be extremely important