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Consider two rigid walls at x=0 and x=L. There is a partition at x=L/2 and the...

Consider two rigid walls at x=0 and x=L. There is a partition at x=L/2 and the particle is in the ground state on the left side of the partition, that is between x=0 and x=L/2. At t=0, the partition is removed. Determine y(x,t) for t ≥ 0
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Answer #1

At t = 0 the wave function is

for 0 < x <L/2

and it is zero

for L/2 < x < L

At a finite time the wave function is in a linear combination of wave function for a particle in a box of length L

Therefore at = 0

Therfore

Substituting for t = 0 value from the first equaiton gives

or

which is zero for even values of n

Therefore

where

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