Question

An electron is confined between *x* = 0 and *x* =
*L*. The wave function of the electron is
*ψ*(*x*) = *A* sin(2*πx*/*L*).
The wave function is zero for the regions *x* < 0 and
*x* > *L*. (a) Determine the normalization
constant *A*. (b) What is the probability of finding the
electron in the region 0 ≤ *x* ≤ *L*/8? {
(2/L)^{1/2}, 4.54%}

Answer #1

The wave function for a particle confined to a one-dimensional
box located between x = 0 and x = L is given by Psi(x) = A sin
(n(pi)x/L) + B cos (n(pi)x/L) . The constants A and B are
determined to be

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(
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