Definitionen der Impulsoperatoren px := psi -> hbar/I*diff(psi,x); py := psi -> hbar/I*diff(psi,y); pz := psi -> hbar/I*diff(psi,z);

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Ortsoperatoren XX := psi -> x*psi; YY := psi -> y*psi; ZZ := psi -> z*psi;

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Drehimpulsoperatoren lx := psi->YY(pz(psi))-ZZ(py(psi)); ly := psi->ZZ(px(psi))-XX(pz(psi)); lz := psi->XX(py(psi))-YY(px(psi));

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lx(psi(x,y,z));ly(psi(x,y,z));lz(psi(x,y,z));

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Drehimpulsquadrat l2 := psi->lx(lx(psi))+ly(ly(psi))+lz(lz(psi));

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collect(simplify(l2(psi(x,y,z))),[x,y,z],distributed);

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Kommutatoren Kom := (a,b,psi)->a(b(psi))-b(a(psi));

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simplify(Kom(lx,ly,psi(x,y,z)));simplify(Kom(ly,lz,psi(x,y,z)));simplify(Kom(lz,lx,psi(x,y,z)));

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simplify(Kom(l2,lx,psi(x,y,z)));simplify(Kom(l2,ly,psi(x,y,z)));simplify(Kom(l2,lz,psi(x,y,z)));

NiMiIiE= NiMiIiE= NiMiIiE=

Zentralsymmetrisch RR := psi-> (x^2+y^2+z^2)^(n/2)*psi;

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simplify(Kom(RR,lx,psi(x,y,z))); simplify(Kom(RR,ly,psi(x,y,z))); simplify(Kom(RR,lz,psi(x,y,z))); simplify(Kom(RR,l2,psi(x,y,z)));

NiMiIiE= NiMiIiE= NiMiIiE= NiMiIiE=