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Physics. involving a change in quantum numbers, permitted by the selection rules:
allowed transition.
to give permission to or for; permit:
to allow a student to be absent; No swimming allowed.
to let have; give as one’s share; grant as one’s right:
to allow a person $100 for expenses.
to permit by neglect, oversight, or the like:
to allow a door to remain open.
to admit; acknowledge; concede:
to allow a claim.
to take into consideration, as by adding or subtracting; set apart:
to allow an hour for changing trains.
Older Use. to say; think.
Archaic. to approve; sanction.
to permit something to happen or to exist; admit (often followed by of):
to spend more than one’s budget allows; a premise that allows of only one conclusion.
allow for, to make concession or provision for:
to allow for breakage.
Contemporary Examples

“It may have allowed Sandy to survive as it got this far north this late in the season,” she says.
Hurricane Sandy’s Unmistakable Message Michael Daly November 4, 2012

On Monday night another group of journalists was allowed to interview her.
Russia’s Partisans Imposing Their Rule in East Ukraine Jamie Dettmer April 21, 2014

And this clique only allowed members with certain rites of entry: liberal Democratic women who were pro-choice.
How Feminism Became the F-Word Amy Siskind January 10, 2009

The two are not allowed to contact each other for the next two years, as she is considered his victim.
Laws Gone Wild: As Teen Sweethearts Go to Prison for Sex, Mothers Rebel Abigail Pesta January 24, 2012

In some countries, fewer people are coming to meetings with U.S. officials, and some are insisting that no notebooks be allowed.
Punching Back at WikiLeaks Howard Kurtz December 6, 2010

Historical Examples

Volunteers were not lacking, and Lancelot and I were allowed to help.
The Boy who sailed with Blake W.H.G. Kingston

Her house is the only one in all Greece where women are allowed to be present at entertainments.
Philothea Lydia Maria Child

These farmers were not allowed to devote their entire time to crop-raising.
Agriculture in Virginia, 1607-1699 Lyman Carrier

Gives her opinion of the force which figure or person may be allowed to have upon her sex.
Clarissa, Volume 1 (of 9) Samuel Richardson

He was allowed to get no further, but was at once asked what a quadruped is.
Talks on the study of literature. Arlo Bates

verb
(transitive) to permit (to do something); let
(transitive) to set aside: five hours were allowed to do the job
(transitive) to let enter or stay: they don’t allow dogs
(transitive) to acknowledge or concede (a point, claim, etc)
(transitive) to let have; grant: he was allowed few visitors
(intransitive) foll by for. to take into account: allow for delays
(intransitive) often foll by of. to permit; admit: a question that allows of only one reply
(transitive; may take a clause as object) (US, dialect) to assert; maintain
(transitive) (archaic) to approve; accept
adj.

late 14c., “praised;” mid-15c., “assigned as a due share;” late 15c., “permitted,” past participle adjective from allow.
v.

early 14c., allouen, “to commend, praise; approve of, be pleased with; appreciate the value of;” also, “take into account or give credit for,” also, in law and philosophy, “recognize, admit as valid” (a privilege, an excuse, a statement, etc.). From late 14c. as “sanction or permit; condone;” in business use from early 15c.

The Middle English word is from Anglo-French alouer, Old French aloer, alloiier (13c.) “allot, apportion, bestow, assign,” from Latin allocare (see allocate). This word in Old French was confused and ultimately merged with aloer; alloer “to praise, commend,” from Latin allaudare, adlaudare, compound of ad- “to” (see ad-) + laudare “to praise” (see laud). From the first word came the sense preserved in allowance as “money granted;” from the second came its meaning “permission based on approval.”

Between the two primary significations there naturally arose a variety of uses blending them in the general idea of assign with approval, grant, concede a thing claimed or urged, admit a thing offered, permit, etc., etc. [OED].

Related: Allowed; allowing.