Derive the Laplacian for a Spherical Coordinate System in 4 Steps

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  1. Andrew
  2. Laplace Operator
  3. Spherical Coordinate System
  4. Del
  5. transport phenomena
  6. transport
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Комментарии
Автор

 Thank you for this video although I had trouble understanding the last few steps. This will help me with my own personal research into the Schrodinger wave equation.

yryu
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Is it always best to choose a coordinate system where the partial derivatives are orthogonal

cameronspalding
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From where is that formula used on setp 4? This is not considered a formula derived from retangular coordinates right? It's much harder this way then what you did

Egonkiller
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I was with you up to step 4, then it gets fuzzy, but maybe I can work it out. Thanks. I am curious about the nexus between step 3's table and step 4.

veganwolf
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Thanks a lot. I worked it out myself and it fits perfectly.

goswamisourabh
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Fun facts: the formula for the gravitational potential energy satisfies this equation, this is true no matter where the entre of mass is, so the total potential which can be calculated by adding the potentials from other planets is also a solution to this equation!

cameronspalding
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I am confused. The vectors in the equation at 2:39 are not unit vectors, no? We applied the equation: UNITVECTOR=VECTOR/n so what is on the numerator is not the unit vector, but the vector itself. Yet we do the scalar multiplication as if it was a unit vector. I would expect in 2:59, for example, that the second term would yield

Either way, I find the notation for VECTORS chosen in the video a little confusing.

jonathanhorton
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Nice! Thanks for that concise derivation of the laplacian. I had been working with it for some time now and I was wondering where it came from. I can't remember ever deriving it in multivariable calculus

lancelovecraft
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l need prove laplacc equation in cylinder

hamsalgifon