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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 ψ(r)=Ae−r/r1,\psi(r)=A \mathrm{e}^{-r / r_{1}}, where AA is a certain constant, r1r_{1} is the first Bohr radius.

Reveal Answer
6.93. φ0=∫(ρ/r)4πr2dr=−e/r1,\varphi_{0}=\int(\rho / r) 4 \pi r^{2} d r=-e / r_{1}, where ρ=−eψ2\rho=-e \psi^{2} is the space charge density, ψ\psi is the normalized wave function.
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