PHY4604 R. D. Field Department of Physics Chapter3_7.doc University of Florida Example: Position and Momentum (2) Transformation from x-rep to p x-rep: To transform from the x-representation ( i.e. position-space) to the p x-representation ( i.e. momentum space) we insert a complete set of |x> states as follows: ∫ ∫ > < = > >< < >= >=< =< dx x x p dx x x p I p p p x x x x x ) ( | | | | | | ) ( ψ where <p x |x> is the “transformation function”. To go the other way around we insert a complete set of |p x > states as follows: ∫ ∫ > < = > >< < >= >=< =< x x x x x x dp p p x dp p p x I x x x ) ( | | | | | | ) ( where <x|p x > = (<p x |x>)* is the “transformation function”. The Transformation Function <x|p x >: This transformation function is arrived at by solving (p x ) op |p x > = p x |p x > or (p x ) op < x|p x > = p x < x|p x > → > < = > < − x x x p x p dx p
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This note was uploaded on 05/29/2011 for the course PHY 4064 taught by Professor Fields during the Spring '07 term at University of Florida.