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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 ψ(r)\psi(r) depends only on rr; (b) the most probable value rprr_{p r} for the ground state of the particle and the probability of the particle to be in the region r<rprr< r_{p r}

Reveal Answer
6.88. (a) ψ(r)=12πr0sin⁡(nπr/r0)r,n=1,2,…\psi(r)=\frac{1}{\sqrt{2 \pi r_{0}}} \frac{\sin \left(n \pi r / r_{0}\right)}{r}, n=1,2, \ldots (b) rpr=r_{p r}= =r0/2;50%=r_{0} / 2 ; 50 \%
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