05_03_07 - Georg.Hoffstaetter@Cornell.edu 75 03/07/2005...

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Unformatted text preview: Georg.Hoffstaetter@Cornell.edu 75 03/07/2005 Orthogonality for different Energies It is a feature of the wave functions of any potential V(x) that the stationary wave functions are orthogonal to each other. E E E x m E x V = + ) ( 2 2 2 2 [ ] = + = dx o dx dx x V dx E E x E x E x E E x E E E x m E E E 2 1 2 1 2 2 2 1 2 2 2 2 2 1 2 1 * * * 2 * * 2 ] ) ( [ + = dx x V dx E E E E x E x m E E ] ) ( [ 2 1 2 1 2 2 1 * * 2 * 2 + = dx x V dx E E E E x E x m E E ] ) ( [ 2 1 2 1 2 2 1 * * 2 * 1 = = = = m n m n nm E E E E E E E E dx dx E E m n if 1 if ) ( * * 2 1 2 1 Georg.Hoffstaetter@Cornell.edu 76 6 Photons and quantum states...
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05_03_07 - Georg.Hoffstaetter@Cornell.edu 75 03/07/2005...

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