Physics 137B, Fall 2007 Problem set 6 : more on methods for time-dependent problems Assigned Friday, 12 October. Due in box Friday, 19 October. 1. For t < 0 a spinless particle is in the ground state of a potential “box” with V = 0 from x = 0 to x = L , and V = ∞ elsewhere. The wavefunction is ψ ( t ) = r 2 L e-iE0 t/ ¯ h sin( πx/L ) . (1) At t = 0 the potential suddenly changes from the box potential to a harmonic oscillator potential centered on x = L/ 2: now the Hamiltonian is H = p 2 2 m + k ( x-L/ 2) 2 / 2 . (2) For time t > 0, ﬁnd using the sudden approximation (a) the probability that the particle is in the ground state, and (b) the probability that the particle is in the ﬁrst excited state. Is either of these nonzero? You may leave any nonzero answer in the form of an integral. 2. Bransden 9.4. The point of this problem is to make you work through the example of a two-level
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This note was uploaded on 08/01/2008 for the course PHYSICS 137B taught by Professor Moore during the Fall '07 term at University of California, Berkeley.