I am taking 0.5-1 mg of Xanax at night occasionally to calm me so I can sleep and I am groggy for the entire next day. Is that normal?

Half life is 12 - 15 hours. There is a post pinned at the top of the benzo forum that has speed of action, and half lifes and another with benzo equivalent dosages.

Yes, it is not unusual to be groggy the next day. Take the smallest dose that works adequately for you. You might try using a pill splitter (as long as you aren't using the extended release form). Also try taking earlier in the evening if it is safe and doesn't interfere with your functioning.

a.m.