All Problems Wave Properties of particles. Schrodinger Equation.
Problem 6.88
From the conditions of the foregoing problem find: (a) normalized eigenfunctions of the particle in the states for which \(\psi(r)\) depends only on \(r\); (b) the most probable value \(r_{p r}\) for the ground state of the particle and the probability of the particle to be in the region \(r< r_{p r}\)
6.88. (a) \(\psi(r)=\frac{1}{\sqrt{2 \pi r_{0}}} \frac{\sin \left(n \pi r / r_{0}\right)}{r}, n=1,2, \ldots\) (b) \(r_{p r}=\) \(=r_{0} / 2 ; 50 \%\)