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Physics 486 FA07 Homework Set 2 Due: Sep 13, 2007 1) The wavefunction of an electron confined to a particular potential V(x) is given by ψ (x)=Aexp(-b|x|), where A and b are constants. (a) Sketch this wavefunction. (b) Find the normalization constant A. (c) Calculate the probability that the electron will be measured in the interval –1/b < x < 1/b. (d) Roughly sketch the potential in which the electron is confined (you’ll be surprised!). 2) Consider the potential below, which roughly describes the potential experienced by an electron confined to a quantum well that is in an electric field. (a) Sketch the four lowest bound state wavefunctions for this potential; pay particular attention to the amplitude and curvature of the wavefunction in and out of the well. (b) Consider the 3 rd energy level. Qualitatively, where is the electron most likely to be observed?

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Unformatted text preview: Please justify your answer. (c) Without trying to solve the Schrödinger equation for this potential, explain how the allowed energies for the electron in this potential will compare to those of the finite square well potential. Be as detailed as possible, and provide your reasoning. x V(x) x = 0 V = 0 x = L V o V(x) ~ eEx 3) An electron in free space is illuminated by light for an interval of Δ t, causing it to move with an energy of about E = 0.1 eV. The uncertainty in its speed is 30m/s. (a) At what approximate speed does it move? (Assume that it is slow enough that you need not take into account relativistic effects.) (b) What is the minimum uncertainty in its position? (c) What is the uncertainty in its energy? (d) What is the minimum amount of illumination time Δ t ?...
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