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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")


    This page titled 4.1: Introduction is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by David M. Hanson, Erica Harvey, Robert Sweeney, Theresa Julia Zielinski via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.