05_04_06 - 118 The energy time uncertainty relation 0.25...

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[email protected] 118 04/06/2005 The energy time uncertainty relation Wave at fixed time t: Wave traveling passed a fixed position x: -40 -20 0 20 40 0.05 0.1 0.15 0.2 0.25 2 0 | ) , ( | t x Ψ 2 0 | ) , ( | t x Ψ 2 group group 1 = E t k x t v k k v x t dk d ϖ Ψ = = Ψ - t t i t i dt e t x x A d e x t x all all 2 ) , ( ) ( 2 ) ( A ) , ( π This uncertainty relation is again due to a Fourier transform , here between time and frequency:
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[email protected] 119 04/06/2005 The shape and width of energy levels τ / 0 ) ( t e N t N - = ϖ E ψ / 2 | ) ( | t e t - A 2 | | A 2 0 2 4 1 0 2 1 2 1 0 2 1 0 0 2 ) ( 1 2 ) ( 1 0 } ) ( { ) ( 1 0 | | ] [ - + - - - - - - - - = = A e dt e e A i i t i t i t i t t i e e t t 0 2 ) ( - - = This is called a Lorentz curve around with full width half max of 0 2 1 = 0 1 2 3 4 0.2 0.4 0.6 0.8 1 eV E 8 10 - !
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This note was uploaded on 09/28/2008 for the course PHYS 316 taught by Professor Hoffstaetter during the Spring '05 term at Cornell.

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05_04_06 - 118 The energy time uncertainty relation 0.25...

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