Question

Assume the wavefunction Ψ(x)=Axe^(-bx^2) is a solution to Schrodinger’s equation for an electron in some potential U(x) over the range -∞<x< ∞.

A) Write an expression which would enable you to find the value of the constant A in terms of the constant b.

B) What is (x)_avg, the average value of x?

C) Write an expression which would enable you to find (x^2)_avg, the average value of x^2 in terms of the constant b.

D) Write an expression which would determine the probability of finding the electron in a region of space - Δx<x< Δx in terms of the constant b.

E) Determine the potential energy U(x) and the energy E associated with Ψ(x) in terms of the constant b and other fundamental constants.

F) Determine the position uncertainty Δx for this electron in terms of the constant b.

G) Determine the probability of finding the electron in a region of space - Δx<x< Δx in terms of the constant b.

Answer 1