4.1: Introduction
- Page ID
- 11125
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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")