# I Derivation of the Laplacian in Spherical Coordinates

1. Jun 12, 2017

### LyleJr

Hi all,

Sorry if this is the wrong section to post this.

For some time, I have wanted to derive the Laplacian in spherical coordinates for myself using what some people call the "brute force" method. I knew it would take several sheets of paper and could quickly become disorganized, so I decided to type it out and present it in what I hope is a logical and obvious manner.

It took me about four days of working in my spare time, but I just finished and thought it might be worth sharing. The Laplacian is something that comes up a lot in textbooks, but never really gets a good explanation of why it is has its final form.

Anyways, here it is. Please excuse any spelling errors. I do think the math is all correct though.

#### Attached Files:

• ###### Derivation of the Laplacian.pdf
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2. Jun 12, 2017

### zwierz

it would be better if you study tensor calculus and get familiar with invariant definition of the Laplace operator: $\Delta=g^{ij}\nabla_i\nabla_j$

3. Jun 12, 2017

### LyleJr

I agree. This was just a for fun exercise to pass the time.

4. Jun 13, 2017

### LyleJr

I found a major mistake on page one, of all places. Corrected version is attached.

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404.9 KB
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32