This integral becomes 0 2 2 / 2 2 /Įquals the second integral on the right. (c) is zero at x =0, and this is the minimum possible probability density.Ġ| | (2/ ) (2/ ). (b) For 0,x we have | |x x= and the probability is given by (1.23) and (A.7) as cxx be = 222 cxbcx e 22 2/ 2 cxx bcxe = 2 22 34 4cx cxbcxe bc x e + = 2 22 36 4cx cxbcxe bc x e +.
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(These statements are valid only for stationary states.)ġ.10 satisfies the time-independent Schrdinger (1.19).
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Substituting into the time-dependent Schrdinger equation and then dividing by, we getĢ 1 2 2 2 2( / )( ) ( /2 )( 2 4 )i ib m bm b m x V = + + = and 2 22V b mx=. For 2 / ,ibt bmxae e = we find / t ib =, 1/ 2 ,x bm x = and 2 2 1 1/ 2 2 ( / )x bm bm x x = Of the expression for 2c into the equation for x gives 21ġ.8 2 2 2( / )( / ) ( /2 )( / )i t m x V = + =. x gt gt t c= + + +v If we know that the particle had position 0x at time 0,t thenĢ10 0 0 0 0 22 ( )x gt gt t c= + + +v and 212 0 0 0 02. xe x x= + + +" For 1,xġ-2 Copyright 2014 Pearson Education, Inc.ġ.7 Integration gives 21 0 0 22 ( ).
#QUANTUM CHEMISTRY 2ND EDITION SOLUTIONS MANUAL SERIES#
(b) The Taylor series for the exponential function is 21 /2!. (c) Since the impure metal has a smaller work function, there will be more energy left over after the electron escapes and the maximum T is larger for impure Na.ġ.5 (a) At high frequencies, we have / 1b Te > and the 1 in the denominator of Plancks formula can be neglected to give Wiens formula.
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The Schrdinger Equation 1.1 (a) F (b) T (c) T. 1-1 Copyright 2014 Pearson Education, Inc.