Question on car battrey/atlernator

I have a 2000 Corolla, and I have been having this problem for a while.
If I dont start the car for a day, the battrey seems to die out. I can jump start it at this point and run it, and it will run okay for the rest of the day. But next day, its gone again.
I had a AAA mechanic look over it, and hes convinced that its NOT the alternator, its the battrey. I took it to WalMart and the mechanic there checked the battrey and said the battrey is okay, its probably the alternator.
The battrey in the car right now is about 3-4 months old.
Can anyone help me out with this?
Thanks a lot.
Shyam

The voltage across the battery should be greater than 13.5V while the engine is running. If not, the alternator or it associated components are faulty. Check the alt belt.

If possible check the electrolite level in the battery. [water]

IMPORTANT: Have the mechanic check to see if there is a current draw on the battery with the key off.

BTW: Autozone will load test your battery at no cost.