Lecture3 - PHYS 360 Quantum Mechanics Fri Lecture 3 Is the...

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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 ar¡cle 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 doesn’t 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 π x L ) e i n π c L ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ t n = 1 ∞ ∑ Thus we can ¡t basically any iniHal string shape by choosing the coefficients 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 Schrödinger (QM) Wave equaHon Eigenvalue equaHon ∂ 2 y ( x , t ) ∂ x 2 = 1 c 2 ∂ 2 y ( x , t ) ∂ t 2 i ∂Ψ ( x , t ) ∂ t = – 2 2 m ∂ 2 Ψ ( x , t ) ∂ x 2 + V Ψ ( x , t ) − 2 2 m d 2 ψ n ( x ) dx 2 + V ψ n ( x ) = E...
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This note was uploaded on 04/23/2011 for the course PHYS 360 taught by Professor Durbin,stephen during the Spring '11 term at Purdue.

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Lecture3 - PHYS 360 Quantum Mechanics Fri Lecture 3 Is the...

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