Problemset_12_Solutions

# Problemset_12_Solutions - [5 A particle of mass m is con F...

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P114 PROBLEM SET 12 Spring 2007 Homework to be handed in by 1700 hours on 24 April 2007 [1] What is the kinetic energy of a proton whose de Broglie wavelength is: (a) 1 nm? (b) 1 fm? [2] Find the wavelength of a bullet with mass 5 g travelling at 600 m/s. Do you think that di f raction e f ects will have a measurable in f uence on the accuracy of the shot? [3] A neutron has kinetic energy of 20 MeV. What size object is necessary to observe neutron di f raction e f ects? Is there anything in nature of this size that could serve as a target to demonstrate the wave nature of 20 MeV neutrons? [4] Suppose that the wavefunction describing the state of an electron predicted a statistical spread in velocity of 2 × 10 6 m/s. What is the corresponding statistical spread in the position of the electron?

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Unformatted text preview: [5] A particle of mass m is con F ned to a tube of length L. (a) Use the Uncertainty Principle to estimate the smallest possible energy. (b) Assume that the inside of the tube is a force-free region and that the particle makes elastic re f ections at the tube ends. Use Schrödinger’s equation F nd the ground-state energy for the particle in the tube. Compare the answer to that of part (a). [6] Consider the second excited state (n=3) in a one-dimensional in F nite square well potential lying between 0 < x < L. (a) What is the expectation value of x? (b) What is the expectation value of x 2 ? [7] The energy of a certain state can be measured with an uncertainty of 2 eV. What is the minimum lifetime of this state? 1...
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Problemset_12_Solutions - [5 A particle of mass m is con F...

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