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A particle is in a box with infinitely rigid walls. The walls are at x = -L/2 and x = +L/2.Show that cn = A cos knx is a possible solution.

A particle is in a box with infinitely rigid walls. The walls are at x = -L/2 and x = +L/2.Show that cn = A cos knx is a possible solution.

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A particle is in a box with infinitely rigid walls. The walls are at x = -L/2 and x = +L/2.Show that cn = A cos knx is a possible solution.

Expert Solution
Step 1

Schrodinger equation of motion is written as

-h22md2ψdx2+vxψ=Eψvx=0, x = -L/2 and x = +L/2∞, otherwise ψ-L2=ψL2=0-h22md2ψdx2=Eψd2ψdx2+K2ψ=0where K2=2mEh2solving the above differential eqaution ,we have solution of the differential equation is ψ=A cos Kx+B sin Kxψ-L2=A cos KL2- B sin KL2=0ψL2=A cos KL2+ B sin KL2=0comparing we getA cos KL2=0B sin KL2=0Both of this cannot be true at the same time .

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