The Requirement of integer orbitals

by Phyzwizz
Tags: integer, orbitals, requirement
Phyzwizz is offline
Feb29-12, 06:53 PM
P: 54
If there is a cloud of electrons around an atom than why can't there be orbitals between 1 and 2 or between 2 and 3. I know the probability of an electron being between certain nodes decreases as they approach them but why as the probabilities go away from the perfect orbital do they not become fractional orbitals? (just starting to learn this stuff)
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TriTertButoxy is offline
Feb29-12, 07:28 PM
P: 194
If you solve the angular part of the Schrödinger equation in the Coulomb potential (or for any spherically symmetric potential), you'll find that in order to satisfy boundary conditions at [itex]\theta=0[/itex] and [itex]\theta=\pi[/itex] and [itex]\phi=0[/itex] and [itex]\phi=2\pi[/itex], you need to have "integer orbitals" (in your language).
Nabeshin is offline
Feb29-12, 07:49 PM
Sci Advisor
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P: 2,194
Simply because there are no (fractional) integers! The orbitals are labeled by their radial quantum number, n, which is an integer. So while an electron in the n=1 orbital has a finite probability of being found at the most probable radius for an electron in the n=2 orbital, and vice versa, they are distinct quantum states.

Jim Kata
Jim Kata is offline
Feb29-12, 08:00 PM
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P: 233

The Requirement of integer orbitals

Anytime you have a bounded system |U|>|E| the eigenvalues will be integral.

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