Can suggests mental or physical ability: "Jane can sing beautifully when she tries." May implies permission or sanction: "Babs may borrow my suitcase if she wishes." This distinction between can and may is illustrated thus: "Jim can swim, but his mother says that he may not." May also expresses possibility and wish (desire): "It may snow tonight (possibility)." "May you have a good rest this weekend (desire)." Might is used after a governing verb in the past tense, may after such a verb in the present tense: "She says that we may go." "She said that we might go."
Dictionary of problem words and expressions. Harry Shaw. 1975.