Skip to main content
Chemistry LibreTexts

1.3: Quantum mechanics

  • Page ID
    75269
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    Bohr's model of the hydrogen atom was all well and good, but it suffered from several shortcomings. It could not explain any other atomic spectra arising from species with more than one electron and its idea of having the electron confined to spherical orbits at certain distances from the nucleus was in conflict with the latest revelations of quantum mechanics.

    DeBroglie

    Louis de Broglie, inspired by Einstein's treatment of light, hypothesized that just as light had wave and particle characteristics, so should matter. What we normally think of as particles also have a wavelength, given by \[ \lambda = \frac{h}{mv} \] where \(lambda\) is the wavelength, \(h\) is Planck's constant (crops up everywhere, doesn't it), \(m\) is the mass, and \(v\) (not to be confused with \(\nu\)) is the velocity. This idea was thought preposterous by many at the time, but after experiments confirmed that matter could behave like waves, by forming interference patterns for example, de Broglie was awarded the Nobel Prize in Physics (1929).

    Heisenberg uncertainty principle

    Around the same time, Werner Heisenberg derived the uncertainty principle: \[ \Delta x \Delta p_x \ge \frac{h}{4\pi} \] where \(\Delta x\) is the uncertainty in the position along the \(x\) coordinate, \(\Delta p_x\) is the uncertainty in the momentum along the \(x\) direction, and \(h\) is Planck's constant. This relationship provides a bound on our knowledge of any system. Specifically one cannot know exactly where a particle is and what its momentum is at the same time; the better you know the better you know the position, the less you know about the momentum and vice-versa.

    Schrödinger

    Rather than orbiting the nucleus at fixed distances, the behavior of the electrons in an atom is given by a wavefunction, \(\psi\), that is a solution to the Schrödinger equation and contains all of the information we can know about that electron. Solving this equation and squeezing information out of these wavefunctions are some of the fundamental activities of this course.


    1.3: Quantum mechanics is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts.

    • Was this article helpful?