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ParticleinBoxEPSolnF2011

# ParticleinBoxEPSolnF2011 - \Px for the particle confined...

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ME 501 Particle in a Box Example Problem Example Problem The normalized, time-independent wave function If/(x) for a particle confined in a box between x = 0 and x = L is given by [2 . (n TrX) ~ = 1,2,3,4, ...... . If/(x) = Vi sm T (a) Determine the probability that the particle will be found between x= 0 and x = L14 for particles in states for which nl = 1 (ground state) and nl = 3 (an excited state). Compare these results with what would be expected for a classical particle confined to the box. (b) Determine the expectation value

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Unformatted text preview: \Px) for the particle confined between x = 0 and x = L. You will need some of the following integrals: J sin 2 (ax)dx ::: __ 1 cos( ax )sin( ax) +lx 2a 2 cos 2 (ax)dx = _1 cos(ax)sin(ax)+lx J 2a 2 sin(ax)cos(ax)dx::: _1sin 2 (ax) J 2a ( <A) p -p -\ r -. I t;q 2A ,'2 c;O I 0 q () '2 I \~--------------------~--------------------------~or VI -:: 3 J ----------\ l-p ~ +-" 0 '2 loS-r · L -C;O () -=, 270 c;-C /qS,SI' cCU{l; / oJ = ,'2 c;-P = T [ -::,~ COS(n:;)Si~(D-~I) + ~J h ~oO ) ------------...
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