Unformatted text preview: Hence, ) ( ) ( ) ( ) ( 2 2 2 2 2 2 x C x mc dx x d c = + − h ) ( ) ( 2 2 2 t C dt t d Φ − = Φ h The time equations is a second order equation with two solutions t C i e t h m = Φ ± ) ( and t C i e x t x h m ) ( ) , ( = Ψ ± . We see that C dx t t x t x i dx t x E t x E op ± = ∂ Ψ ∂ Ψ = Ψ Ψ >= < ∫ ∫ ∞ ∞ − ± ∗ ± ∞ ∞ − ± ∗ ± ) , ( ) , ( ) , ( ) , ( h C dx t t x t x dx t x E t x E op = ∂ Ψ ∂ Ψ − = Ψ Ψ >= < ∫ ∫ ∞ ∞ − ± ∗ ± ∞ ∞ − ± ∗ ± 2 2 2 2 2 ) , ( ) , ( ) , ( ) , ( h Hence 2 2 = > < − > < = Δ E E E and E C = . 2 nd order differential equation!...
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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.
 Spring '07
 FIELDS
 mechanics, Mass

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