Going to 3rd year:want to spherical harmonic

[Brown Arrow]

Going to 3rd year:want to "spherical harmonic"

I'm going on to my 3rd year in university, my professor recommended that i should learn spherical harmonic over the summer...he told me to wiki it but that turned out to be a mess for me.. i have take first year calculus for physicist, and 2nd year differential equation, and vector calculus.

Vector calculus part one:
Partial derivatives, gradient, tangent plane, Jacobian matrix and chain rule, Taylor series; extremal problems, extremal problems with constraints and Lagrange multipliers, multiple integrals, spherical and cylindrical coordinates, law of transformation of variables.

Vector calculus part two:
Introduction to Fourier expansions
Paths, path integrals
Vector fields, line integrals, define differential form, Green’s Theorem
Surfaces (parametrized), surface integrals, Divergence Theorem
Differential forms, Stokes’ Theorem (general and special case in R3 )
Introduction to the calculus of variations

so basically i just wanted to know where to get started, recommended books, online lech etc

Thanks in advance for you contribution

Arrow

 

[jowens1988]

In what context is he wanting you to learn them? Are we talking about in the context of the angular portion of the solution to the three dimensional Schrödinger equation?

If that's the case, I think Griffith covers it pretty well in his Quantum Mechanics text.

I think the article on Mathworld is pretty good, too, and has the advantage over Griffiths in that it is free:

http://mathworld.wolfram.com/SphericalHarmonic.html.

I don't think you really need anything besides (ordinary) differential equations to understand the derivation. Both Mathworld, Griffiths, and the first few Google results simply give you the $$\Theta(\theta)$$ portion of the solution, and do not show you how it is obtained. I don't know if this is a problem, or not. Either way, hopefully this will get you started.

 

[Brown Arrow]

well its for future physics courses, so I'm not really sure, he just said learn spherical harmonics

 

[MissSilvy]

Pfft, spherical harmonics are not that bad. I guess a book on special functions would be overkill (like Dover's book) but Griffiths Quantum does cover it very well, like Jowens said. There's not incredibly much to learn, but I think it is easier to deal with if you took linear algebra first and learn spherical harmonics along with quantum mechanics.

 

[jowens1988]

There's not incredibly much to learn, but I think it is easier to deal with if you took linear algebra first and learn spherical harmonics along with quantum mechanics.

I agree. If we're talking about math needed to prepare for a quantum mechanics course, I would brush up on my differential equations and linear algebra.

I really cannot imagine that it would be too helpful to learn about spherical harmonics before you see them in quantum mechanics; I never did, and I had no problems understanding them.

 

[Brown Arrow]

i will look into my griffits book i have

thanks for the replies