Ground State of Hydrogen

Classical Mechanics Level 3

Compute the radial wavefunction of an electron in the ground state of hydrogen.

Note: recall that $\rho = \dfrac{rme^2}{4\pi \epsilon_0 \hbar^2 n}$ for $n$ the energy level of the electron.

\left(\frac{\rho}{2r}\right)^{3/2} e^{-\rho}

\left(\frac{\rho}{r}\right)^{1/2} e^{-2\rho}

\frac12 \left(\frac{\rho}{r}\right)^{3/2} e^{-\rho/2}

2\left(\frac{\rho}{r}\right)^{3/2} e^{-\rho}