The probability of of finding the particle between L/4 and 3L/4 is
P=β«β£Ξ¨β£2dx
=L2ββ«4Lβ43Lβββ£sin(LnΟxβ)β£2dx
=L1ββ«4Lβ43Lβββ£1βcos(L2nΟxβ)β£dx
=L1β[xβ(L2nΟβ)1βsin(L2nΟxβ)] between limits L/4 and 3L/4
=L1β[43Lββ(L2nΟβ)1βsin(L2nΟ(43Lβ)β)β([4Lββ(L2nΟβ)1βsin(L2nΟ(4Lβ)β))]
=[21ββ2nΟ1β(β1)3n+2nΟ1β(β1)n]
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