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Unformatted text preview: Physics 4141 Test 1 February 28, 2007 Answer all questions on a separate sheet of paper, showing as many steps as possible. Think about partial credit! 1. An electron confined to x > 0 has the wave function ( x,t ) = Axe- x/ 2 e- iEt/ h x ( x,t ) = 0 x < In terms of the parameter : a. What is A such that the wave function is normalized? Answer : A 2 integraltext x 2 e- x dx = 1 , A = radicalbig 3 / 2. b. What restriction can you place on ? Answer: > 0. (Technically, real part of must be > 0.) c. What is ( x ) ( t )? Answer : ( x ) ( t ) = A 2 integraltext x 3 e- x dx, (time-independent!) = 3! 2 = 3 / . 2. At t = 0 a particle of mass m in a harmonic oscillator potential is described by the state vector ( x, 0) = A [ ( x ) + 2 2 ( x )] where n ( x ) are the SHO states. a. Normalize ( x, 0). Answer: A = 1 / 5. b. Calculate ( p ) ( t ) Answer: ( p ) = d dt ( x ) = 0 because ( x ) is a constant (namely, zero). This can be seenis a constant (namely, zero)....
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