Consider the following wave functions (over all space - not the infinite square well!):
\(\psi_a(x) = A e^{-x^2/3}\)
\(\psi_b(x) = B \frac{1}{x^2+2} \)
\(\psi_c(x) = C \;\mbox{sech}\left(\frac{x}{5}\right)\) (“sech” is the hyperbolic secant function.)
In each case:
- normalize the wave function,
- plot the wave function using Mathematica or other computer plotting tool (be sure to include the code you used and label your plots/axes appropriately),
- find the probability that the particle is measured to be in the range \(0<x<1\).