HrmOscEx

HrmOscEx - Harmonic Oscillator-Excited States 2 d2 h V(x 2m dx2 V(x = V(x = 1/2 kx2 1 22(x = A e/2 x x 1(x = polynomial(x polynomial has one zero

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Harmonic Oscillator-Excited States h 2 2m d 2 dx 2 Ψ + V(x) Ψ=ΕΨ V(x) = 1 / 2 kx 2 Ψ ο (x) = A e 1 / 2 α 2 x 2 V(x) x Ψ 1 (x) = polynomial * Ψ ο (x) polynomial has one zero: ax + b E = h ν o ( v + 1 / 2 ) y = α x Ψ ο (y) = A e 1 / 2 y 2 polynomial = H v (y) d 2 H v dy 2 - 2y dH v dy + 2v H v = 0 Hermite Polynomials v H v (y) H v ( α x) 0 11 1 2y 2 α x 2 4y 2 - 2 4 α 2 x 2 - 2 3 8y 3 - 12y 8 α 3 x 3 - 12 α
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This document was uploaded on 02/22/2012.

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