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Chemistry LibreTexts

4.0: 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