- #1

fluidistic

Gold Member

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In the Schrödinger's equation, one considers the Hamiltonian operator as [itex]-\frac{\hbar }{2m} \nabla ^2 +V (\vec r, t )[/itex]. From classical mechanics we know that in a central force problem, the motion is constrained into a plane. My question is thus: why is the Laplacian taken in spherical coordinates (this assumes a 3d motion) instead of polar coordinates (this assumes a motion constrained into 2 dimensions)?