Is my Zebra Finch really happy?

I know that Finches are social birds so I am so confused. We had a pair of Zebra Finches. The female died almost three weeks ago. Now the male is hoping around the cage, singing all the time, plays on his swing, talks to the bird in the mirror. He still drinks, takes baths, and eats. It just seems like he is happier now than he was. Do we dare just leave him without a mate or a friend?