# pset2 - to characteristic physical dimensions Then...

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Spring Term 2003 22.02 Introduction to APPLIED NUCLEAR PHYSICS Problem Set #2 1. Particle in 1D box: Consider a free particle moving in box as shown in gure with in nite potential bounding the box at x =0 and x = L . V(x) X X=0 X= L ˆ a. Solve the energy eigenvalue problem, H ψ n = E n ψ n , and give a complete listing of both the normalized eigenfunctions, ψ n , and the energy spectrum, E n . b. Also for state ψ = ψ n , as in b), write the probability that a position measurement nds the particle within the interval, x ,about x ? Besuretogetyouranswer dimensionally correct for a probablility. c. Now suppose the system is in a superposition quantum state: ψ ( x )= a 1 ψ 1 ( x )+ a 3 ψ 3 ( x )

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i) What are the possible outcomes of an energy measurement in this case? ii) Determine a 1 and a 3 if the probability of nding E = E 1 is P 1 = . 1, and the probability of measuring, E = E 3 is P 3 = . 9. 2 iii) What is the probability of nding the particle at x = 3 L ? Can you state more speci cally what the measurement is? 2. Calculate the de Broglie wavelength of a 10-eV electron, and a 10-MeV alpha particle. Relate the numbers you obtain
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Unformatted text preview: to characteristic physical dimensions. Then calculate the de Broglie wavelength for a 10-g bullet moving at a speed of 1,000 m/sec. What velocity would the bullet be going if its de Broglie wavelength were 10 − 8 cm? Give the velocity in approximate atomic displacements per year . (You may take 10 − 8 cm. to be the unit of atomic displacements.) 3. Libo f , problem: 7.42 4. A neutron of energy 20 Mev is incident on a square barrier of height 40 Mev and width, 10 F (Fermi). What is the tunneling probability for the neutron to penetrate the barrier? ( You do NOT have to do a complete detailed estimate for this problem. Just estimate the tunneling probability and put in the numbers)....
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pset2 - to characteristic physical dimensions Then...

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