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Problem Set 3

# Problem Set 3 - C so that ψ is properly normalized Now...

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PHYSICS 230 – PROBLEM SET 3 PHYSICS 230 1. Read Shankar Section 5.1. Do Problem 5.1.3. Read Shankar Chapter 6. 2. At time t = 0 the initial state of a free particle on a line is given by the sum of two identical gaussian wave packets of width Δ separated by a distance L . Assume Δ is smaller than L . ψ ( x ) = C (exp( - ( x - L/ 2) 2 / 2 ) + exp( - ( x + L/ 2) 2 / 2 )) Determine
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Unformatted text preview: C so that ψ is properly normalized. Now calculate the time evolution of the wavefunction, ψ ( x,t ). The discussion in Shankar pages 153-4 may be useful. Plot the probability | ψ ( x,t ) | 2 at early, medium and late times. What is the characteristic time when things get interesting in this problem?...
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