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Deriving the Laplacian in spherical coordinates

Thread starter PhysicsIzHard
Start date Nov 4, 2012
Tags

Coordinates Laplacian Spherical Spherical coordinates

1 reply · 3K views · last reply Nov 5, 2012

PhysicsIzHard

Thread starter
Nov 4, 2012

#1

Homework Statement

Printed homework page on the Laplacian in spherical coordinates, showing two forms of the Laplacian formula and two spherical coordinate diagrams with x, y, z axes, r, theta and phi, and the equations x = r sin theta cos phi, y = r sin theta sin phi, z = r cos theta.

Printed homework sheet with parts (b) to (e) on spherical coordinates: showing the derivative of the unit vector r-hat with respect to theta is orthogonal to it, the theta-hat and phi-hat unit vector relations, and the gradient in spherical coordinates.

Printed worksheet on spherical coordinates: parts (f) and (g) with partial derivative identities for unit vectors, the gradient in spherical form, and the Laplacian target formula with a hint.

Homework Equations

All above.

The Attempt at a Solution

Tried the first few, couldn't get them to work. Any ideas, hopefully for each step?

Discussion

clamtrox

Nov 5, 2012

#2

For a, you should remind yourself of trigonometric identities involving right triangles.

For b, how long is a unit vector?

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