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HW-3 - (b Use the uncertainty principle to estimate the...

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Physics 17 Due 10-16-09 Fall 2009 T. Tomboulis HOMEWORK # 3 Reading Assignment: SMM Ch. 5. (Subsection ’The Electron Microscope’ in section 5.2 is optional material. You may also find it useful to review the basics of wave motion, interference and diffraction in your PH 1 text.) Problems: 1. SMM Ch. 5: Problem #10 2. SMM Ch. 5: Problem #16 3. A wave packet is given by f ( x, t ) = Z -∞ dk A ( k ) e i ( kx - q k 4 t ) (1) with A ( k ) = ( sin( k a ) : 0 k 0 : otherwise (2) where q , a are constants. (a) What is the group velocity of this wave packet? (b) A second wave packet is described by the same distribution A ( k ) of k ’s except that a in (2) is changed to b , with b > a . What is the group velocity now? (c) Which of the two packets is more localized in space? 4. SMM Ch. 5: Problem #20. Comment on the size of the answer. 5. SMM Ch. 5: Problem #24 6. (a) A particle of mass m is confined in a 1-dimesional box (i.e. a segment of the x -axis) of length L . Use the uncertainty principle to estimate its energy.
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Unformatted text preview: (b) Use the uncertainty principle to estimate the ground state energy o± a harmonic oscillator. The harmonic oscillator energy is given by: E = p 2 2 m + 1 2 mω 2 x 2 Hint: Follow the same procedure as in Problem 5 (SMM #24) above. 1 7. SMM Ch. 5: Problem #34 8. In a double slit electron experiment with slits of unequal width, the following is observed. There is, of course, no interference pattern if one of the slits is kept closed. If slit #2 is closed the intensity (number of electrons) of the observed maximum on the screen behind slit #1 is 16 times larger than the intensity observed behind slit #2 when the experiment is repeated with slit #1 closed. Consider now the interference pattern observed when both slits are open. What is the ratio I max /I min of the intensities I max and I min seen, respectively, at the maxima and minima of the interfernece pattern? 2...
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