may和might可以表示可能性和许可。might的语气比may较婉转。此外，may也可以接动词的完成形式，表示可能、说不定已经做某事。
【例如】
I thought it might be difficult for me to learn advanced mathematics. (可能性)
May I come in, sir? (许可)
She may have gone to the hospital.
Research findings show we spend about two hours dreaming every night, no matter what we ____during the day. (CET-4 1999,1)
A) must have done
B) should have done
C) would have done
D) may have done
情态动词后面加动词完成式，有不同意义。
must have done表示一定做过某事；
should have done表示本应该做某事，含有批评的意思；
would have done主要用于虚拟语气，表示对过去的虚拟；
may have done表示可能已经作过某事。
根据句意：研究结果表明，我们每晚有两个小时做梦，不管白天可能做了什么，情态动词后表示可能性，故答案应为D。