486_HW4 - Physics 486 FA07 Homework Set 4 Due 1 Based on...

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Physics 486 FA07 Homework Set 4 Due: Sep 27, 2007 1) Based on Griffiths 2.37 . An electron in an infinite square well potential occupying the region 0 x L has the initial wavefunction Ψ (x,0) = A sin 3 ( π x/L) within the same region. (a) Determine the constant A. Hint: sin m α and cos m α can be reduced by repeated application of trigonometric sum formulas to linear combinations of sin(n α ) and cos(n α ), n=0,1,2,3. . (b) Find the time-dependent wavefunction Ψ (x,t). (c) What is the expectation value of position ‹x› as a function of time? (d) What is the expectation value of the energy in terms of the ground state energy E 1 ? If the length of the well is L = 3nm, what is the value of this expectation in electron volts? (e) If a measurement is made on the energy of the particle, what are/is the possible outcome(s) and with what proability/ies? 2) Momentum representation. In last week’s homework, you considered an electronic wavefunction given by ψ (x)=N/(x 2 +a 2

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486_HW4 - Physics 486 FA07 Homework Set 4 Due 1 Based on...

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