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 fnd it use±ul to review the basics o± wave motion, inter±erence and di²raction 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 o± this wave packet? (b) A second wave packet is described by the same distribution A ( k ) o± k ’s except that a in (2) is changed to b , with b > a . What is the group velocity now? (c) Which o± the two packets is more localized in space? 4. SMM Ch. 5: Problem #20. Comment on the size o± the answer. 5. SMM Ch. 5: Problem #24 6. (a) A particle o± mass m is confned in a 1-dimesional box (i.e. a segment o± the x -axis) o± 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 m 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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HW-3 - (b) Use the uncertainty principle to estimate the...

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