Skip to main content
Physics LibreTexts

3: One-Dimensional Potentials

  • Page ID
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)

    • 3.1: The Free Particle
      Before we begin our exploration of the quantum mechanics of a particle bound by a potential well, we need to examine the simpler case where the particle is not bound at all.
    • 3.2: Infinite Square Well
      We return to the all-purpose model of the particle-in-a-box, to see how our new-found formalism fits into something with which we are already familiar.
    • 3.3: Harmonic Oscillator
      We continue our review of one-dimensional potential wells with the simple harmonic oscillator potential.
    • 3.4: Finite Square Well
      We now look at a square well whose boundary conditions make it more difficult to solve than the infinite square well, but which has features that make it a better model for real physical systems.
    • 3.5: Tunneling
      We conclude our discussion of one-dimensional quantum mechanics with a look at the phenomenon of tunneling. This is a natural extension of the wave function "leaking" into classically-forbidden regions of potentials.

    3: One-Dimensional Potentials is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Tom Weideman directly on the LibreTexts platform.

    • Was this article helpful?