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# p828aps8 - Physics 828 Problem Set VIII Dr Stroud Due...

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Physics 828: Problem Set VIII Dr. Stroud Due Wednesday, March 6,2008 by 11:59 P. M. Each problem is worth 10 pts. unless otherwise specified. 1. Shankar, exercise 18.4.2. 2. Shankar, exercise 18.4.4. 3. (20 pts.) A hydrogen atom is initially in its 1s state. A uniform electric field E cos( ωt ) is applied to the atom. Calculate the ionization rate as a function of ω . You may assume that the final states are free-particle states, and also that the proton is infinitely massive. 4. (20pts.) Time-Dependent Schr¨odinger equation, two-level sys- tem, resonant perturbation. In this problem, you will obtain a (nearly) exact solution to the time-dependent Schr¨odinger equation for a certain special case. As was discussed in class, the solution of the time-dependent Schr¨odinger equation can be written in the form | ψ ( t ) ) = summationdisplay n c n ( t ) | φ n ) , (1) where the | φ n ) are a complete orthonormal basis, and the c n ( t )’s are a set of time-dependent coefficients. Let us assume that the Hamiltonian of the system is H = H 0 + W ( t ), where H 0 is a time-independent

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