Editing Node (physics) (section)

===Waves in two or three dimensions===
[[File:HAtomOrbitals.png|thumb|Radial and angular nodes on hydrogen wavefunctions.]]

In two dimensional standing waves, nodes are curves (often straight lines or circles when displayed on simple geometries.) For example, sand collects along the nodes of a vibrating [[Ernst Chladni|Chladni plate]] to indicate regions where the plate is not moving.<ref>Comer, J. R., et al. [https://aapt.scitation.org/doi/pdf/10.1119/1.1758222 "Chladni plates revisited."] American journal of physics 72.10 (2004): 1345-1346.</ref>

In chemistry, [[quantum mechanics|quantum mechanical]] waves, or "[[atomic orbital|orbitals]]", are used to describe the wave-like properties of electrons. Many of these quantum waves have nodes and antinodes as well. The number and position of these nodes and antinodes give rise to many of the properties of an atom or [[covalent bond]]. Atomic orbitals are classified according to the number of radial and angular nodes. A radial node for the hydrogen atom is a sphere that occurs where the [[wavefunction]] for an atomic orbital is equal to zero, while the angular node is 
a flat plane.<ref>Supplemental modules (physical and Theoretical Chemistry). Chemistry LibreTexts. (2020, December 13). Retrieved September 13, 2022, from https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)</ref>

[[Molecular orbital]]s are classified according to bonding character. Molecular orbitals with an antinode between nuclei are very stable, and are known as "bonding orbitals" which strengthen the bond. In contrast, molecular orbitals with a node between nuclei will not be stable due to electrostatic repulsion and are known as "anti-bonding orbitals" which weaken the bond. Another such [[quantum mechanics|quantum mechanical]] concept is the [[particle in a box]] where the number of nodes of the wavefunction can help determine the quantum energy state&mdash;zero nodes corresponds to the ground state, one node corresponds to the 1st excited state, etc. In general,<ref>[[Albert Messiah]], 1966. ''Quantum Mechanics'' (Vol. I), English translation from French by G. M. Temmer. North Holland, John Wiley & Sons. Cf. chpt. IV, section III. [https://archive.org/details/QuantumMechanicsVolumeI   online]  Ch 3  §12</ref> ''If one arranges the eigenstates in the order of increasing energies, <math>\epsilon_1,\epsilon_2, \epsilon_3,...</math>, the eigenfunctions likewise fall in the order of increasing number of nodes; the ''n''th eigenfunction has ''n−1'' nodes, between each of which the following eigenfunctions have at least one node''.