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A particle is located in a unidimensional square potential well with infinitely high wall. The width of the well is l. Find the normalized wave fucntions of the stationary states of the particle taking the midpoint of the well for the origin of the x coordinate. |
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Answer» Solution :Here `-(l)/(2)le(l)/(2)`. Again we have `Psi(x)=B "cos" (SQRT(2)mE)/( ħ)+A "SIN" sqrt(2mEx)/( ħ)` Then the BOUNDARY conditions `Psi(+-(l)/(2))=0` gives even solution. Here `sqrt(2mE)=(2N+1)(pi ħ)/(l)` and `E_(n)=(2n+1)^(2)(pi^(2) ħ^(2))/(2ml^(2))` `Psi_(n)^(e )(x)sqrt((2)/(l))cos (2n+1)(pi x)/(l)` `n= 0,1,2,3`.... This solution is even under `xrarr-x` (2) `B=0` `sqrt(2mEl)/(2ħ)=n pi,n=1,2`.... `E_(n)=(2npi)^(2)(ħ^(2))/(2ml^(2))` `Psi_(n)^(0)=sqrt((2)/(l))"sin"(2n pix)/(l),n=1,2`.... This solution is odd. |
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