Consider a fictitious one-dimensional system with one electron. The wave function for the electron, drawn at the top of the next page, is Ï(x) =

Consider a fictitious one-dimensional system with one electron. The wave function for the electron, drawn at the top of the next page, is ψ(x) = sin x from x = 0 to x = 2π.
(a) Sketch the probability density, ψ2(x), from x = 0 to x = 2π.
(b) At what value or values of x will there be the greatest probability of finding the electron?
(c) What is the probability that the electron will be found at x = π? What is such a point in a wave function called?

2 0 0