Hydrogen Atom

Quantum Mechanics · Part 4

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Table of Contents

  1. 1.The Coulomb Potential
  2. 2.Radial Equation
  3. 3.Energy Levels
  4. 4.Bohr Radius
  5. 5.Quantum Numbers and Degeneracy
  6. 6.Radial Wave Functions
  7. 7.First Few States
  8. 8.Spectroscopic Notation
  9. 9.Selection Rules
  10. 10.Radial Probability Distribution

Key Equations

$$V(r) = -\frac{e^2}{4\pi\epsilon_0 r} = -\frac{ke^2}{r}$$
$$E_n = -\frac{me^4}{2(4\pi\epsilon_0)^2\hbar^2 n^2} = -\frac{13.6 \text{ eV}}{n^2}$$
$$g_n = \sum_{\ell=0}^{n-1}(2\ell+1) = n^2$$
$$\psi_{200} = \frac{1}{4\sqrt{2\pi a_0^3}}\left(2-\frac{r}{a_0}\right)e^{-r/(2a_0)}$$

Equations are rendered with MathJax in the PDF with professional LaTeX typesetting.

Course Context

This PDF is part of the Quantum Mechanics course on CoursesHub.World. Master quantum mechanics from mathematical foundations to advanced topics. Covers Hilbert spaces, wave functions, angular momentum, perturbation theory, scattering, and path integrals with 450+ pages ...

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