Editing Matter wave (section)

=== Standing matter waves ===
{{See also|Standing wave}}
[[File:InfiniteSquareWellAnimation.gif|thumb|200px|right|Some trajectories of a particle in a box according to [[Newton's laws]] of [[classical mechanics]] (A), and matter waves (B–F). In (B–F), the horizontal axis is position, and the vertical axis is the real part (blue) and imaginary part (red) of the [[wavefunction]]. The states (B,C,D) are [[energy eigenstate]]s, but (E,F) are not.]]
The third class are matter waves which have a wavevector, a wavelength and vary with time, but have a zero [[group velocity]] or [[probability flux]]. The simplest of these, similar to the notation above would be
<math display="block">\cos(\mathbf{k}\cdot\mathbf{r} - \omega t)</math>
These occur as part of the [[particle in a box]], and other cases such as in a [[Particle in a ring|ring]]. This can, and arguably should be, extended to many other cases. For instance, in early work de Broglie used the concept that an electron matter wave must be continuous in a ring to connect to the [[Bohr–Sommerfeld quantization|Bohr–Sommerfeld condition]] in the early approaches to quantum mechanics.<ref>{{Cite book |last=Jammer |first=Max |title=The conceptual development of quantum mechanics |date=1989 |publisher=Thomas publishers |isbn=978-0-88318-617-6 |edition=2nd |series=The history of modern physics |location=Los Angeles (Calif.)}}</ref> In that sense [[atomic orbital]]s around atoms, and also [[molecular orbital]]s are electron matter waves.<ref>{{Cite journal |last=Mulliken |first=Robert S. |date=1932 |title=Electronic Structures of Polyatomic Molecules and Valence. II. General Considerations |url=https://link.aps.org/doi/10.1103/PhysRev.41.49 |journal=Physical Review |volume=41 |issue=1 |pages=49–71 |doi=10.1103/PhysRev.41.49 |bibcode=1932PhRv...41...49M |url-access=subscription }}</ref><ref>{{Cite book |last=Griffiths |first=David J. |title=Introduction to quantum mechanics |date=1995 |publisher=Prentice Hall |isbn=978-0-13-124405-4 |location=Englewood Cliffs, NJ}}</ref><ref>{{Cite book |last=Levine |first=Ira N. |title=Quantum chemistry |date=2000 |publisher=Prentice Hall |isbn=978-0-13-685512-5 |edition=5th |location=Upper Saddle River, NJ}}</ref>