CH01 Notes

32 continuous variables probability vs probability

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Unformatted text preview: d deviation : spread about 〈 〉 √〈( ) 〉 : the measure of the 6 〈( ) 〉 ∑( ) ∑( () √〈 〉 ∑( 〈 〉) 〈 〉〈 〉 〈〉 〈〉 1.3.2 continuous variables Probability ( ) vs. probability density ( ( )) ∫ ∫ () () : normalization ∫ ∫ () 〈〉 ()() 〈( () 〈〉) () 〈〉 ∑ Or () )〉 〈 ( )〉 〈 7 〉 〈〉 〈〉 〈〉 ( Problem 1-3) ( ) ∫ 〈〉 ) ( ( | ∫( ( ∫ 〉 ) ) () ∫ ∫( ∫( ) ) ∫ √〈 〉 ( ) ( ( ∫ ( ∫ () ∫ ) 2nd moment: 〈 ) √ () Normalization : ∫ [∫ ) ) ) ( ) √ Standard deviation : 1 〈〉 √ 1.4 normalization ∫|( )| Presence of particles anywhere and anytime: normalizable ( square-integrable) Does ( ) stay normalized as time goes on if it is normalized at ? Or, ∫ |( )| ∫|( )| ∫ ∫( |( )| ) & |( )| ∫|( )| [ ( ( 2 )] )| since ( ) will be vanished as exists somewhere) . (or, particle partial integration ∫ ∫ 3 1.5 Momentum 〈〉 |( ∫ )| How to connect this average 〈 〉 with experimental data? 〈 〉 : the average of measurements performed on particles all in the state ( by the collapse of wavefunction). Repeated measu...
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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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