Question

Prove $f(\xi)$ behaves as $e^{\xi^2}$ if $\lambda<0$ in $\frac{d^2f}{d\xi^2}-2\xi\frac{df}{d\xi}+2\lambda f(\xi)=0$

score 153 · Answer 1 · 2020-12-17 14:40:29

153

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Prove $f(\xi)$ behaves as $e^{\xi^2}$ if $\lambda<0$ in $\frac{d^2f}{d\xi^2}-2\xi\frac{df}{d\xi}+2\lambda f(\xi)=0$

Published on 17 Dec 2020 - 14:40

score 202 · Answer 2 · 2020-12-22 22:29:22

202

Views

Spectrum and point spectrum of quantum harmonic oscillator

Published on 22 Dec 2020 - 22:29

score 108 · Answer 3 · 2021-01-03 19:03:22

108

Views

Proving that $\int_{-\infty}^{\infty}x^{m}e^{-x^2}H_n(x)dx=0$ for $m$ an integer and $0\leq m\leq n-1$

Published on 03 Jan 2021 - 19:03

score 383 · Answer 4 · 2021-01-04 14:35:41

383

Views

Problem proving $\int_{-\infty}^{\infty}x^2e^{-x^2}H_n(x)H_m(x)dx$

Published on 04 Jan 2021 - 14:35

score 172 · Answer 5 · 2021-01-04 16:00:45

Proving that the $2n$ Hermite polynomial is $H_{2n}(x)=(-1)^n\sum_{s=0}^{n}(-1)^{2s}(2x)^{2s}\cfrac{(2n)!}{(2s)!(n-s)!}$

score 40 · Answer 6 · 2021-01-04 21:22:38

40

Views

How is the formula $H_{2n+1}(x)=(-1)^n\sum_{s=0}^{n}(-1)^s(2x)^{2s+1}\cfrac{(2n+1)!}{(2s+1)!(n-s)!}$ derived?

Published on 04 Jan 2021 - 21:22

score 597 · Answer 7 · 2021-01-05 02:37:55

597

Views

Formulas's deduction from the generating function of Hermite polynomials

Published on 05 Jan 2021 - 2:37

score 129 · Answer 8 · 2021-01-11 04:28:43

129

Views

Integral Involving Hermite Polynomial and rational function

Published on 11 Jan 2021 - 4:28

score 133 · Answer 9 · 2021-01-15 05:49:32

133

Views

Expanding Dawson's integral in a series of Hermite functions

Published on 15 Jan 2021 - 5:49

score 72 · Answer 10 · 2021-01-21 00:39:11

72

Views

Prove that $\int_{-\infty}^{\infty} e^{-x^2} H_m(x)H_n(x)dx$

Published on 21 Jan 2021 - 0:39

score 251 · Answer 11 · 2021-01-22 12:39:19

251

Views

Construction of Hermite Polynomials

Published on 22 Jan 2021 - 12:39

score 123 · Answer 12 · 2021-02-08 05:10:37

123

Views

Term-by-term differentiation for the generating function of the Hermite polynomial

Published on 08 Feb 2021 - 5:10

score 329 · Answer 13 · 2021-02-16 02:19:31

329

Views

How to calculate Hermite interpolation without slope in the end points (unknown derivatives)?

Published on 16 Feb 2021 - 2:19

score 193 · Answer 14 · 2021-02-24 00:45:26

193

Views

Hermite polynomials from binomial theorem

Published on 24 Feb 2021 - 0:45

score 122 · Answer 15 · 2021-02-24 14:30:21

122

Views

Help with the Hermite differential equation

Published on 24 Feb 2021 - 14:30

List Question

Prove $f(\xi)$ behaves as $e^{\xi^2}$ if $\lambda<0$ in $\frac{d^2f}{d\xi^2}-2\xi\frac{df}{d\xi}+2\lambda f(\xi)=0$

Spectrum and point spectrum of quantum harmonic oscillator

Proving that $\int_{-\infty}^{\infty}x^{m}e^{-x^2}H_n(x)dx=0$ for $m$ an integer and $0\leq m\leq n-1$

Problem proving $\int_{-\infty}^{\infty}x^2e^{-x^2}H_n(x)H_m(x)dx$

Proving that the $2n$ Hermite polynomial is $H_{2n}(x)=(-1)^n\sum_{s=0}^{n}(-1)^{2s}(2x)^{2s}\cfrac{(2n)!}{(2s)!(n-s)!}$

How is the formula $H_{2n+1}(x)=(-1)^n\sum_{s=0}^{n}(-1)^s(2x)^{2s+1}\cfrac{(2n+1)!}{(2s+1)!(n-s)!}$ derived?

Formulas's deduction from the generating function of Hermite polynomials

Integral Involving Hermite Polynomial and rational function

Expanding Dawson's integral in a series of Hermite functions

Prove that $\int_{-\infty}^{\infty} e^{-x^2} H_m(x)H_n(x)dx$

Construction of Hermite Polynomials

Term-by-term differentiation for the generating function of the Hermite polynomial

How to calculate Hermite interpolation without slope in the end points (unknown derivatives)?

Hermite polynomials from binomial theorem

Help with the Hermite differential equation

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