Question

Why is Legendre's polynomial the solution to the theta equation in the Schrödinger's equation of a hydrogen atom?

score 1k · Answer 1 · 2026-03-22 20:00:39

1k

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Why is Legendre's polynomial the solution to the theta equation in the Schrödinger's equation of a hydrogen atom?

Published on 22 Mar 2026 - 20:00

score 130 · Answer 2 · 2026-03-19 16:51:43

130

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Calculate Stieltjes Polynomial

Published on 19 Mar 2026 - 16:51

score 1.6k · Answer 3 · 2026-03-23 11:50:29

1.6k

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How do I turn $\cos(3\theta)$ into a polynomial?

Published on 23 Mar 2026 - 11:50

score 239 · Answer 4 · 2026-03-22 08:21:45

239

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Legendre polynomials: show that two algorithms construct the same polynomials

Published on 22 Mar 2026 - 8:21

score 355 · Answer 5 · 2026-03-23 04:29:48

355

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Asymptotic form of the associated Legendre polynomials $P^m_l (z)$ at z=1

Published on 23 Mar 2026 - 4:29

score 243 · Answer 6 · 2026-03-22 18:26:04

243

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Calculating coefficient of approximation polynomial which is expanded in to a series of Legendre Polynomials

Published on 22 Mar 2026 - 18:26

score 3.7k · Answer 7 · 2026-03-22 16:46:03

3.7k

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Proving orthogonality of Legendre polynomials

Published on 22 Mar 2026 - 16:46

score 9.1k · Answer 8 · 2026-03-22 23:43:39

9.1k

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If $P_n(1)=1$ calculate $P'_n(1)$ in Legendre polynomials

Published on 22 Mar 2026 - 23:43

score 221 · Answer 9 · 2026-03-22 22:00:23

221

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Proving a result related to Legendre polynomials

Published on 22 Mar 2026 - 22:00

score 1.1k · Answer 10 · 2026-03-22 19:39:50

1.1k

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How to prove that Legendre polynomials satisfy $P_n(x)\leq 1$

Published on 22 Mar 2026 - 19:39

score 1.4k · Answer 11 · 2026-03-23 06:12:27

1.4k

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Legendre Polynomials form a Basis

Published on 23 Mar 2026 - 6:12

score 787 · Answer 12 · 2026-03-22 05:21:06

787

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Higher order Legendre's linear differential equation

Published on 22 Mar 2026 - 5:21

score 286 · Answer 13 · 2026-03-22 02:19:49

286

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If $P_n$ is $n$th Legendre polynomial and $|x|\leqslant1$ then $\frac{1-x^2}{n^2}(P'_n)^2+P^{2}_{n} \le 1$

Published on 22 Mar 2026 - 2:19

score 94 · Answer 14 · 2026-03-21 23:49:52

94

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Evaluating $\sum\limits_{k=0}^n \frac{(-1)^k (4 n - 2 k)!}{k! (2 n - k)! (2 n - 2 k)! (2 n + 2 r + 1 - 2 k)}$

Published on 21 Mar 2026 - 23:49

score 67 · Answer 15 · 2026-03-22 03:52:08

67

Views

why does $n$ have to be an integer in order for the solutions to be bounded?

Published on 22 Mar 2026 - 3:52

List Question

Why is Legendre's polynomial the solution to the theta equation in the Schrödinger's equation of a hydrogen atom?

Calculate Stieltjes Polynomial

How do I turn $\cos(3\theta)$ into a polynomial?

Legendre polynomials: show that two algorithms construct the same polynomials

Asymptotic form of the associated Legendre polynomials $P^m_l (z)$ at z=1

Calculating coefficient of approximation polynomial which is expanded in to a series of Legendre Polynomials

Proving orthogonality of Legendre polynomials

If $P_n(1)=1$ calculate $P'_n(1)$ in Legendre polynomials

Proving a result related to Legendre polynomials

How to prove that Legendre polynomials satisfy $P_n(x)\leq 1$

Legendre Polynomials form a Basis

Higher order Legendre's linear differential equation

If $P_n$ is $n$th Legendre polynomial and $|x|\leqslant1$ then $\frac{1-x^2}{n^2}(P'_n)^2+P^{2}_{n} \le 1$

Evaluating $\sum\limits_{k=0}^n \frac{(-1)^k (4 n - 2 k)!}{k! (2 n - k)! (2 n - 2 k)! (2 n + 2 r + 1 - 2 k)}$

why does $n$ have to be an integer in order for the solutions to be bounded?

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