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# HW5 - = 0 is given by ψ x,0 = x ≤ C sin π x L for 0<...

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PHYSICS 4455 — QUANTUM MECHANICS Problem Set 5 — due 10 / 6 / 2005, in class. 1. One-dimensional problems. Liboff Problem 3.23 Liboff Problem 4.1 2. Dirac notation and operators Liboff Problem 4.4 Liboff Problem 4.12 3. Extra credit: The time evolution operator for a “particle in a box”. Here, we consider the time evolution of an initial wave function, for the Schrödinger equation describing a particle in a one-dimensional box, i.e., V ( x ) = x 0 0 for 0 < x < L x L The initial state ψ( x , t ) at time t = 0 is given by
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Unformatted text preview: = 0 is given by ψ( x ,0 ) = x ≤ C sin π x L for 0 < x < L / 2 x ≥ L / 2 C is a constant of normalization. Find the wave function ψ( x , t ) for t > 0. Hint: Write the time evolution operator in the x-representation, using the energy eigenvalues and eigenfunctions associated with this potential, and evaluate the necessary integral. Which of the eigenfunctions contribute to ψ( x , t ) ? You should read: Liboff, Chapters 4 and 5....
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