Abarim Publications' online Biblical Greek Dictionary
The particle αν (an) is peculiar to Greek, a curious one, and unlike anything that exists in modern English. It appears to be most active in the ghostly hyperspace of the Greek language, reacting to and causing verbal moods, and slightly altering the core essence of verbs, like a benevolent virus that enters words and flicks a fraction of its genes on or off. Walter Bauer says: "it denotes that the action of the verb is dependent on some circumstance or condition" (A Greek-English Lexicon of the New Testament and Other Early Christian Literature). It's even so versatile that after careful study, scholars have concluded that its usage in the New Testament is not wholly consistent with its usage in other Greek texts.
Our particle mostly evokes the optative and subjunctive verbal moods, which express situations supposed, expected or wished (something might or ought to be), and when it comes with a straight forward indicative mood (something is), it still introduces a situation that would have been if something else hadn't. It promises realization of things suggested, vowed or foretold, and assures certainty about results even when the how and when of the implied process is shrouded in uncertainty.
Our particle appears to augment or emphasize situations that are also carried by the words it accompanies, and is as such rarely translated or translatable. The full width and compass of this elfish particle has provided material for many a dissertation, and although we here at Abarim Publications never stray from encouraging people to pursue the great mysteries of this earth, we also find it unlikely that the Creator has hidden life-saving instructions exclusively in the deepest caverns of our particle's ecosphere.
Our particle has one derivation: the conjunction εαν (ean), which combines our word with the conditional conjunction ει (ei), meaning if. Our particle εαν (ean) means something like "if it would" or "if it is as it ought to be". It occurs frequently in the New Testament, but its subtle difference with the unbound particle of condition ει (ei) is demonstrated in Matthew 4:9, where the devil promises Jesus to hand over all the kingdoms if He "could kindly" submit to him "as He ought to". Of course, the validity of any supposition lies entirely in the eye of the beholder, and, as told, Jesus saw validity rather in not submitting.