NRQM10_5

# NRQM10_5 - Physics 216 Problem Set 5 Spring 2010 DUE JUNE 8...

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Unformatted text preview: Physics 216 Problem Set 5 Spring 2010 DUE: JUNE 8, 2010 FINAL EXAM ALERT: The final exam will be take place from 11 am–2 pm on Wednesday June 9, 2010 in ISB 235. Please note the change of date, time and location. The exam will cover the entire course. During the exam, you may consult Shankar and Baym, your class notes (and any other handwritten notes), and any of the homework solutions and class handouts that are posted on the course website. 1. Tritium (the isotope H 3 ), which is initially in its ground state, undergoes spon- taneous beta decay, emitting an electron of maximum energy of about 17 keV. The nucleus remaining is He 3 . (a) Calculate the probability that the electron of this ion is left in a quantum state of principal quantum number n = 2. (b) What is the probability that the electron of this ion is left in quantum state with ℓ negationslash = 0 ? In this problem, you should neglect nuclear recoil. Note the energy of the emitted electron. What is the relevant approximation? Explain. 2. Consider a two-level system with E 1 < E 2 . There is a time-dependent potential that connects the two levels as follows: V 11 = V 22 = 0 , V 12 = γe iωt , V 21 = γe − iωt ( γ real) , where V ij = ( i | V | j ) . At time t = 0, it is known that only the lower level is populated— that is, c 1 (0) = 1 and c 2 (0) = 0. Note that a general state of the system can be expressed as a linear combination of eigenstates of the unperturbed Hamiltonian (in the Schrodinger picture): | ψ ( t ) ) = 2 summationdisplay n =1 c n ( t ) e − iE n t/ planckover2pi1 | n ) (a) Starting with the time-dependent Schrodinger equation, derive the following...
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NRQM10_5 - Physics 216 Problem Set 5 Spring 2010 DUE JUNE 8...

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