Thursday, 22 August 2019

quantum mechanics - Normalizing a set of eigenfunctions with different domains



Maybe it seems so easy, but it is not!



How can we obtain the normalization constant N for a set of eigenfunctions with different domains?


For example, we have


ψ1=N(f1eκx+g1eκx),x[0,1],ψ2=N(f2eκx+g2eκx),x[0,1],ψ3=N(f3eκx+g3eκx),x[1,0],ψ4=N(f4eκx+g4eκx),x[1,0]..


we can normalize each wavefunction by the integral x2x1ψψdx=1, but that way, the other eigenfunctions are not normalized to one!




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