Question: Consider a particle moving in a scalar potentialV ( v e c ( r ) ) = V z ( x ) + V y

Consider a particle moving in a scalar potentialV(vec(r))=Vz(x)+Vy(y)+(V)z(z)
a)Show that the Hamiltonian can be written as:
(H)=(H)x+(H)y+(H)n, where (H)z=(p)z22m+Vz(x)(similarly for (H)y and ((H)z

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