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(a) The normalised eigenfunction for the lowest energy eigenvalue is ., and is such that < Þo, Vo >= 1. Find explicitly the normalisation constant N where a²x² v. (2) = N exp (-) and a =

(a) The normalised eigenfunction for the lowest energy eigenvalue is ., and is such that < Þo, Vo >= 1. Find explicitly the normalisation constant N where a²x² v. (2) = N exp (-) and a =

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(a) The normalised eigenfunction for the lowest energy eigenvalue is vo, and is such that < Vo, Vo >= 1. Find explicitly the normalisation constant N where a²x? v. (r) = N oxp (-) %3D 2 mw and a = (b) Find the normalised first excited state energy eigenfunction, w1 (x), using the raising d operator D4 – y, where y = ax. dy - (c) A particle in this harmonic oscillator potential has a normalised wavefunction 1/2 V (y) 1 + 4 y ) exp where y = ax. Find the probability that a measurement of the energy of the particle will give the lowest energy eigenvalue. You may assume that L exp (-g°) dy = Vñ, L* exp (-v°) dy = .
Transcribed Image Text:(a) The normalised eigenfunction for the lowest energy eigenvalue is vo, and is such that < Vo, Vo >= 1. Find explicitly the normalisation constant N where a²x? v. (r) = N oxp (-) %3D 2 mw and a = (b) Find the normalised first excited state energy eigenfunction, w1 (x), using the raising d operator D4 – y, where y = ax. dy - (c) A particle in this harmonic oscillator potential has a normalised wavefunction 1/2 V (y) 1 + 4 y ) exp where y = ax. Find the probability that a measurement of the energy of the particle will give the lowest energy eigenvalue. You may assume that L exp (-g°) dy = Vñ, L* exp (-v°) dy = .
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