Spherical Harmonics Equation
Tags: #math #spherical harmonicsEquation
$$[\frac{1}{\sin \theta} \frac{\partial}{\partial \theta}(\sin \theta \frac{\partial}{\partial \theta}) + \frac{1}{\sin^{2} \theta} \frac{\partial^{2}}{\partial \phi^{2}}) ] Y^{m}_{l} + l(l+1) Y^{m}_{l}=0 \\ Y^{m}_{l}(\theta,\phi)=\sqrt{\frac{2l+1}{4 \pi} \frac{(l-|m|)!}{(l+|m|)!}}P^{m}_{l}(\cos \theta) e^{im \phi} \times \begin{cases}(-1)^{m} & m\ge 0 \\ 1 & m <0 \end{cases}$$Latex Code
[\frac{1}{\sin \theta} \frac{\partial}{\partial \theta}(\sin \theta \frac{\partial}{\partial \theta}) + \frac{1}{\sin^{2} \theta} \frac{\partial^{2}}{\partial \phi^{2}}) ] Y^{m}_{l} + l(l+1) Y^{m}_{l}=0 \\ Y^{m}_{l}(\theta,\phi)=\sqrt{\frac{2l+1}{4 \pi} \frac{(l-|m|)!}{(l+|m|)!}}P^{m}_{l}(\cos \theta) e^{im \phi} \times \begin{cases}(-1)^{m} & m\ge 0 \\ 1 & m <0 \end{cases}
Have Fun
Let's Vote for the Most Difficult Equation!
Introduction
Explanation
- Spherical Harmonics Equation
- Spherical Harmonics Solution :
Related Documents
Discussion
Comment to Make Wishes Come True
Leave your wishes (e.g. Passing Exams) in the comments and earn as many upvotes as possible to make your wishes come true
-
Sara DuncanHoping to get over the hurdle of this exam.Denise Richardson reply to Sara DuncanGooood Luck, Man!2023-11-13 00:00:00.0 -
Timothy CookIt's my mission to pass this test.Judy Bell reply to Timothy CookYou can make it...2023-11-19 00:00:00.0 -
Heather AdamsPlease universe, let me pass this exam.Connie Bishop reply to Heather AdamsBest Wishes.2023-11-22 00:00:00.0
Reply