Lecture3 - PHYS 360 Quantum Mechanics Fri Jan 14, 2011...

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Unformatted text preview: PHYS 360 Quantum Mechanics Fri Jan 14, 2011 Lecture 3: Is the Moon really there when nobody looks? Download arcle with this tle (by David Mermin, in Physics Today) from the course web site. Homework Set #1 due in class, Monday Jan 24 Chapter 1: #3, 4, 5, 14, 16. L But, our string doesnt look like a sine funcHon. We learned from Fourier analysis, however, that we can construct this shape from combinaHons: y ( x , t ) = a n sin( n x L ) e i n c L t n = 1 Thus we can t basically any iniHal string shape by choosing the coecients a n correctly. The eigenfuncHons f n (x) make up the normal modes or the standing wave soluHons of the wave equaHon. ! From last Hme(?) L Vibra&ng String Schrdinger (QM) Wave equaHon Eigenvalue equaHon 2 y ( x , t ) x 2 = 1 c 2 2 y ( x , t ) t 2 i ( x , t ) t = 2 2 m 2 ( x , t ) x 2 + V ( x , t ) 2 2 m d 2 n ( x ) dx 2 + V n ( x ) = E...
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Lecture3 - PHYS 360 Quantum Mechanics Fri Jan 14, 2011...

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