# 4.1: Introduction


## 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

David M. Hanson, Erica Harvey, Robert Sweeney, Theresa Julia Zielinski ("Quantum States of Atoms and Molecules")

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