- #1
Izzhov
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I'm currently working out the Schrödinger equation for a proton in a constant magnetic field for a research project, and while computing the Hamiltonian I came across this expression:
[itex](\vec{A}\cdot\nabla)\Psi[/itex]
where [itex]\Psi[/itex] is a scalar function of r, theta, and phi. How do you evaluate this expression in spherical coordinates in terms of the components of [itex]\vec{A}[/itex] and derivatives of [itex]\Psi[/itex]?
[itex](\vec{A}\cdot\nabla)\Psi[/itex]
where [itex]\Psi[/itex] is a scalar function of r, theta, and phi. How do you evaluate this expression in spherical coordinates in terms of the components of [itex]\vec{A}[/itex] and derivatives of [itex]\Psi[/itex]?