Postpartum depression is a very real thing that a lot of women go through after giving birth. Lots of things contribute to postpartum depression from a feeling of despair from no longer being pregnant to being upset because her body still looks as though she is. Some estimate that as much as 90% of women will go through some form of postpartum depression at some point after delivery. Most of the time the postpartum depression will go away without the aid of medication. Hormonal changes play a big factor in postpartum depression. Even though the depression may not be that severe, it is a very real and emotional problem that your wife is facing. You should respect that she cannot simply "cheer up" and that you can play a key role in helping her through the period of depression.
Help combat her fatigue. Make sure that you give your wife all the support that she might need. Offer to take over duties around the house like laundry or cooking. Offer to do diaper changing duty or take over some of the baby's feedings too. If you can't be around to help her, enlist the help of family or friends. Often having a new baby around means not a lot of time for mommy to get some much needed rest. Make time for her to relax and take a nap or two.
A little positive support goes a long way. You may not realize it but new moms go through a wide range of emotions during the postpartum period. Women often feel unattractive or like they have no idea what they are doing. She may feel neglected now that the shift of attention has dramatically shifted from her onto the new arrival. It's important that you spend time with your wife and compliment her often on her appearance or on her mothering abilities. Small, unexpected gifts can sometimes help to lift her spirits too.
Get away for a bit. Just because you have a new baby around doesn't mean your life as a couple is over. Encourage (but don't force) your wife to allow grandma or some other trusted adult to care for the baby for a short period of time. Spend some time alone with her away from the house and the baby whenever possible. Even if you can only get out once a week or once every other week, it will make a difference. Make sure that you spend alone time with her every day. Even if you can just curl up with her while she takes a nap, your presence is important.
Give her something to look forward to. If you can, plan a trip or a vacation for sometime in the future. Make sure that you plan it for some period in the future when you think baby and mom will be ready.
If the period of postpartum depression is interfering with your wife's sleep or appetite or is accompanied by thoughts of hopelessness, extreme anger or violence, seek professional help for her right away. Never wait for the depression to go away on it's own if you have any concerns at all. It never hurts to speak to a doctor if you have any questions.