Processing math: 100%
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Generalization to 3D

Key idea:

V=VxVyVz

Repeated outer tensor product of multiple vectors.

a(q)=(a(q)0,,a(q)Nq),q=0,,mp=a(0)a(m)pi0,i1,,im=a(0)i1a(1)i1a(m)im

ψp,q,r(x,y,z)=ˆψp(x)ˆψq(y)ˆψr(z)u(x,y,z)=pIxqIyrIzcp,q,rψp,q,r(x,y,z)

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