Module 3: Linear Harmonic Oscillator-I
3.1 Let n x represents the normalized eigenfunctions corresponding to the linear harmonic
oscillator problem n 0,1, 2,3.... . 0 exp 1 2 ; and .
x N 2 x
Determine the normalization constant N.
(a) N (b)
N 2 (c)
N 2 (d) N [Answer (d)]
3.2 Let n x represents the normalized eigenfunctions corresponding to the linear harmonic oscillator problem n 0,1, 2,3.... . Let , 0 = 1 ψ0 + 1ψ5 + 5 ψ9
2 15
3
x x x i x
represents the wavefunction at t 0. If we make a measurement of energy, then the probability of finding the value 11
2 will be (a) 0
(b) 1 4 (c) 1
3 (d) 1
2 [Answer (b)]
3.3 Let n x represents the normalized eigenfunctions corresponding to the linear harmonic oscillator problem n 0,1, 2,3.... . Let , 0 = 1 ψ0 + 1ψ5 + 5 ψ9
2 15
x 3 x x i x
represents the wavefunction at t 0. If we make a measurement of energy, then the probability of finding the value 7
2 will be (a) 0
(b) 1 4 (c) 1
3 (d) 1
2 [Answer (a)]
