# 4.1: Introduction

- Page ID
- 11125

## Overview of key concepts and equations for the particle in a box

Potential energy | V = 0 inside box (0 < x < L) V = ∞ outside box |

Hamiltonian | \(\hat {H} = -\frac {\hbar ^2}{2m} \frac {d^2}{dx^2}\) |

Wavefunctions | \({(\frac {2}{L})}^{1/2} \sin (\frac {n\pi}{L}x)\) |

Quantum Numbers | n = 1, 2, 3, … |

Energies | \(E = n^2 (\frac {h^2}{8mL^2})\) |

Spectroscopic Selection Rules | Δn = odd integer |

Angular Momentum Properties | none |

### Contributors

- Adapted from "Quantum States of Atoms and Molecules" by David M. Hanson, Erica Harvey, Robert Sweeney, Theresa Julia Zielinski