Chapter 7 Lecture 3D

Chapter 7 Lecture 3D - Chapter 7- 3 Dimensional Quantum...

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Chapter 7- 3 Dimensional Quantum Mechanics 7-2 Fundamental Concepts ! ! 2 2 m " 2 # ( " r , t ) + V ( " r ) ( " r , t ) = i ! $ $ t ( " r , t ) Schrodinger Equation ( " r , t ) 2 dV = 1 Normalization % $ $ t ( " r , t ) + " " i J ( " r , t ) = 0 Continuity Equation Operator commutation relations [ x i , x i ] = 0 [ p i , p i ] = 0 [ x i , p i ] = i ! ! ij Cartesian Coordinates E = p x 2 2 m + p y 2 2 m + p z 2 2 m + V ( x , y , z ) ! ! 2 2 m ( " x 2 + " y 2 + " z 2 ) ( r ) + V ( x , y , z ) ( x , y , z ) = E ( x , y , z ) " i = $ x i , ( x , y , z ) = ( x ) ( y ) ( z ) ! ! 2 2 m '( y ) ''( z ) " x 2 ( x ) + ( x ) ''( z ) " y 2 '( y ) + '( y ) ''( z ) " z 2 ''( z ) ( ) + V ( x , y , z ) ( x ) '( y ) ''( z ) = E ( x ) '( y ) ''( z ) If the potential energy term can be factorized as V ( x , y , z ) = + V ( x ) + V ( y ) + V ( z ) then the 3 D equation can be solved by separation of var iables int o 3 1 D equations
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This note was uploaded on 09/13/2009 for the course PHYS 451 taught by Professor Cavaglia,m during the Fall '08 term at Ole Miss.

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Chapter 7 Lecture 3D - Chapter 7- 3 Dimensional Quantum...

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