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Unformatted text preview: 40 CHAPTER 4. SINGLE-PARTICLE SYSTEMS 18.104.22.168 Solution angub-b Question: What is the magnetic quantum number of a macroscopic, 1 kg, particle that is encircling the z-axis at a distance of 1 m at a speed of 1 m/s? Write out as an integer, and show digits you are not sure about as a question mark. Answer: Showing all digits as a question mark is not acceptable, of course. The classical angular momentum is 1 m distance times 1 kg times 1 m/s, or 1 J s. Since that should be m ¯ h with m the magnetic quantum number, you get m = 1 J s 1 . 054 , 57 10 − 34 J s = 9 , 482 , 3?? , ??? , ??? , ??? , ??? , ??? , ??? , ??? , ??? , ??? 22.214.171.124 Solution angub-c Question: Actually, based on the derived eigenfunction, C ( r, θ ) e i mφ , would any macroscopic particle ever be at a single magnetic quantum number in the first place? In particular, what can you say about where the particle can be found in an eigenstate? Answer: The square magnitude of the wave function gives the probability of finding the particle. The square magnitude, vextendsingle vextendsingle vextendsingle C ( r, θ ) e i mφ vextendsingle vextendsingle vextendsingle 2 = | C ( r, θ...
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This note was uploaded on 11/13/2011 for the course PHY 4458 taught by Professor Garvin during the Fall '11 term at University of Florida.
- Fall '11