HW 03(1)

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Unformatted text preview: ψ ( x ) = The wave function is zero elsewhere. Calculate the probability of finding the electron between (a) 0 < x < a/4, (b) a/4 < x < a/2, (c) –a/2 < x < a/2. The expectation value of x is given by 2 x= a x2 x !πx$ !πx$ ! 2π x $+ 1 2( ∫ cos # a & x cos # a & dx = a ∫ *1 + cos # a &- x dx "% "% " %, x1 x1 ) x ! 2π x $ 2 1 1 x xa = x x2 − sin # &+ " a % x1 2π a 1 a 2π x2 ! 2π x $ & dx a% ∫ sin # " x1 x2 ! 2 π x2 $ ! 2π x1 $+ ! 2π x $ x −x 1( 1a = 2 1− cos # & − x1 sin # &- + & * x2 sin # "a% " a %, ( 2π ) 2π "a% a 2π ) x 1 = ! 2 π x2 $ ! 2π x1 $+ ! 2π x1 $+ x2 − x1 1 ( a ( !...
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This document was uploaded on 01/28/2014.

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