olutions independent of

olutions independent of - independent of and we shall have...

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olutions independent of and Initially we shall just restrict ourselves to those cases where the wave function is independent of and , i.e., (11.8) In that case the Schrödinger equation becomes (why?) (11.9) One often simplifies life even further by substituting , and multiplying the equation by at the same time, (11.10) Of course we shall need to normalise solutions of this type. Even though the solution are
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Unformatted text preview: independent of and , we shall have to integrate over these variables. Here a geometric picture comes in handy. For each value of , the allowed values of range over the surface of a sphere of radius . The area of such a sphere is . Thus the integration over can be reduced to (11.11) Especially, the normalisation condition translates to...
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