Editing Atomic orbital (section)

=== Modern conceptions and connections to the Heisenberg uncertainty principle ===
Immediately after [[Werner Heisenberg|Heisenberg]] discovered his [[uncertainty principle]],<ref>{{cite journal|last=Heisenberg| first=W.|title=Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik|journal=[[Zeitschrift für Physik A]] |date=March 1927| volume=43 | pages=172–198|doi=10.1007/BF01397280|bibcode = 1927ZPhy...43..172H| issue=3–4| s2cid=122763326}}</ref> [[Niels Bohr|Bohr]] noted that the existence of any sort of [[wave packet]] implies uncertainty in the wave frequency and wavelength, since a spread of frequencies is needed to create the packet itself.<ref>{{cite journal|last=Bohr | first=Niels| title=The Quantum Postulate and the Recent Development of Atomic Theory|journal=Nature |date=April 1928| volume=121 | pages=580–590|doi=10.1038/121580a0 |bibcode = 1928Natur.121..580B| issue=3050 |doi-access=free}}</ref> In quantum mechanics, where all particle momenta are associated with waves, it is the formation of such a wave packet which localizes the wave, and thus the particle, in space. In states where a quantum mechanical particle is bound, it must be localized as a wave packet, and the existence of the packet and its minimum size implies a spread and minimal value in particle wavelength, and thus also momentum and energy. In quantum mechanics, as a particle is localized to a smaller region in space, the associated compressed wave packet requires a larger and larger range of momenta, and thus larger kinetic energy. Thus the binding energy to contain or trap a particle in a smaller region of space increases without bound as the region of space grows smaller. Particles cannot be restricted to a geometric point in space, since this would require infinite particle momentum.

In chemistry, [[Erwin Schrödinger]], [[Linus Pauling]], Mulliken and others noted that the consequence of Heisenberg's relation was that the electron, as a wave packet, could not be considered to have an exact location in its orbital. [[Max Born]] suggested that the electron's position needed to be described by a [[probability distribution]] which was connected with finding the electron at some point in the wave-function which described its associated wave packet. The new quantum mechanics did not give exact results, but only the probabilities for the occurrence of a variety of possible such results. Heisenberg held that the path of a moving particle has no meaning if we cannot observe it, as we cannot with electrons in an atom.

In the quantum picture of Heisenberg, Schrödinger and others, the Bohr atom number&nbsp;''n'' for each orbital became known as an ''n-sphere''{{citation needed|date=January 2013}} in a three-dimensional atom and was pictured as the most probable energy of the probability cloud of the electron's wave packet which surrounded the atom.