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# test3a - Physics 463 Final Exam Your grade will be based...

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Physics 463 - Final Exam Your grade will be based upon your answers to 4 of the following 6 problems. If you turn in more than 4 solutions, your 4 highest scores will be used to compute your f nal exam grade. 1. Let {| n x ,n y ,n z i} denote the eigenstates of an isotropic 3D oscillator of frequency ω centered at the origin, where n x denotes the number of vibrational quanta associated with Cartesian coordinate x . (i) Determine, at least to f rst order, the splitting of the threefold degenerate n =1 states | 1 , 0 , 0 i| 0 , 1 , 0 i| 0 , 0 , 1 i due to a weak perturbation V = α m ω 2 xz. (Recall, in 1 D, q = x p m ω / ¯ h .) 2. A particle in one dimension is in the single bound state φ 0 ( x )= qe q | x | of an attractive delta function potential V = αδ ( x ) , in which q = m α / ¯ h 2 , and the bound state energy is ε B = ¯ h 2 q 2 / 2 m. Aharmon ic perturbation of the form V = V 0 cos( k 0 x )cos( ω t ) is applied to the system. Find the transition rate for ionizing transitions to free particle states φ
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