All Problems Wave Properties of particles. Schrodinger Equation.
Problem 6.93
Find the mean electrostatic potential produced by an electron in the centre of a hydrogen atom if the electron is in the ground state for which the wave function is \(\psi(r)=A \mathrm{e}^{-r / r_{1}},\) where \(A\) is a certain constant, \(r_{1}\) is the first Bohr radius.
6.93. \(\varphi_{0}=\int(\rho / r) 4 \pi r^{2} d r=-e / r_{1},\) where \(\rho=-e \psi^{2}\) is the space charge density, \(\psi\) is the normalized wave function.