CH01 Notes

then 4 time evolution momentum

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Unformatted text preview: rements on same ensemble the expectation value 〈 〉 is the average of repeated measurement on an ensemble of identically prepared system no velocity concept like in classical Mechanics since is not defined in Assume now that 〈 〉 in orthodox position. 〈〉 , then : 4 〈〉 ∫ [ ∫|| ( ) ∫ )] time-evolution : || ∫( ∫ 〈〉 momentum: 〈 〉 ( ∫ ( Kinetic energy : ) Angular momentum 〈( )〉 (order of operator) ∫ ( ) Example) For classical quantity corresponding operator? ( 〈 〉) ) , what is ( Not clear. 5 ) Ehrenfest’s theorem : expectation value obeys the classical laws. 〈〉 ∫ ∫( ) ∫( ) ∫ (( ) ( )) 〈 ∫ 6 〉 1.6 The Uncertainty principle Where is the wave? Sinusoidal wave : wavelength is well-defined, but not position. Bump (packet): position is well-defined, but not de Broglie formula, since ( ) Heisenberg’s uncertainty principle precise measurements on each position and momentum measurement, not simultaneous. 7...
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This note was uploaded on 03/31/2012 for the course PHYS 4141 taught by Professor Schaefer during the Spring '07 term at LSU.

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