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Given a particle of mass m in the harmonic oscillator potential starts out in the state mwx2 mw p(x, 0) = A 1 2 exp 2h with Hermite polynomials H, (E) = 1, H, (E) = 2E, H2(E) = 48? – 2. Find the coefficients cn of p (x, 0) in the basis mw 4 1 E2 то Pn (x) = πή VZm(€) exp(-) ; E = 2"n!

Given a particle of mass m in the harmonic oscillator potential starts out in the state mwx2 mw p(x, 0) = A 1 2 exp 2h with Hermite polynomials H, (E) = 1, H, (E) = 2E, H2(E) = 48? – 2. Find the coefficients cn of p (x, 0) in the basis mw 4 1 E2 то Pn (x) = πή VZm(€) exp(-) ; E = 2"n!

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With the given Hermite polynomials how to find the coefficients cn?

Given a particle of mass m in the harmonic oscillator potential starts out in the state тох? mw Ф(х, 0) — А( 1- 2 = exp 2h with Hermite polynomials Ho (E) = 1, H, (E) = 2E, H,(E) = 4E² - 2. Find the coefficients c, of y (x, 0) in the basis mw 1/4 1 то P, (x) VZ",) exp) th V2"n! 2 by expressing 2 mw 1- 2 in terms of the first three Hermite polynomials H, (E), H, (E), and H2(E).
Transcribed Image Text:Given a particle of mass m in the harmonic oscillator potential starts out in the state тох? mw Ф(х, 0) — А( 1- 2 = exp 2h with Hermite polynomials Ho (E) = 1, H, (E) = 2E, H,(E) = 4E² - 2. Find the coefficients c, of y (x, 0) in the basis mw 1/4 1 то P, (x) VZ",) exp) th V2"n! 2 by expressing 2 mw 1- 2 in terms of the first three Hermite polynomials H, (E), H, (E), and H2(E).
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