05_02_21 - [email protected] 48 Qualitative...

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Unformatted text preview: [email protected] 48 Qualitative plots of bound-state wave functions 02/21/2005 ● The wave function of the ground state has, in the classically allowed region with E > V , the smallest possible “curvature”: 2 ) ( 2 ) ( / ) ( ’ ’ V E m x x-- = Φ Φ ● The wave function of the ground state has, in the classically forbidden region with E < V , the fastest exponential falloff: 2 ) ( 2 ) ( / ) ( ’ ’ ✁ E V m x x- = Φ Φ x ) ( x V E Φ ● For continuous potentials, the wave function is continuous in its first 2 derivatives. ● The stationary state n has n nodes: ) ( = Φ node x x ) ( x V 1 E 1 Φ [email protected] 49 The amplitude of the wave function 02/21/2005 Regions of smaller k have larger maximum values of the amplitude than adjacent regions of larger k . x 2 Φ 2 E Smoothness at center: 12 Φ x 12 E ) ( x V ) ( x V 2 2 2 2 ) ( ’ 2 ) ( ’ 2 2 2 ) ( ) ( ) cos( ) cos( ) ( ’ ) sin( ) sin( ) ( L R k c k c L R R R R R L L L L R R R L L L...
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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 University (Engineering School).

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05_02_21 - [email protected] 48 Qualitative...

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