ph2a_quiz4

# ph2a_quiz4 - Ph002a Fall 2009 Quiz 4 Due 24 November 2009...

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Ph002a, Fall 2009 Quiz 4 Due: 24 November 2009 Preliminary note: You should be able to do this problem by hand, but you should feel free to use a calculator, Mathematica, or any other symbolic- manipulation program if you ﬁnd it easier to evaluate integrals or numbers that way. Consider a quantum-mechanical particle of mass m in a harmonic potential V ( x ) = (1 / 2) 2 x 2 , where ω is the oscillator frequency, and the spatial coordinate x spans the range -∞ < x < . Suppose furthermore that someone tells you that at some particular time, the spatial part of the wave function is ψ a ( x ) = ± A ( a 2 - x 2 ) for | x | < a, 0 , for | x | > a, (1) where A is a normalization constant, and a is a distance. For reasons that will become clear below, we will refer to ψ a ( x ) as a “trial wave function”. Note that ψ a ( x ) is not an eigenstate (i.e., it is not a stationary state), but we will not be considering time evolution so this should not concern you. 1. Calculate the constant

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ph2a_quiz4 - Ph002a Fall 2009 Quiz 4 Due 24 November 2009...

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