Kitten is hyperactive during playtime ( sometimes for hours )

We adopted a kitten a three weeks ago. Our little one is now almost 15 weeks old.  First day, she settled in nicely. She didn't hide under the furniture, she explored ran and even came to cuddle on our lap.

At night she is quiet and settles somewhere in the appartment and sleeps. We don't wake up at night so we think she is sleeping or at least very calm and quiet during the night.

When we wake up, we try and play 30 to 60 minutes with her, to tire her out when we are going to work. In the morning her activity level is what I would call normal for a kitten. She plays, runs around, chases her mouse, ... 

When we return home, after about 6-7- hours, she hears the keys turn and you can hear her running towards the door to greet us. At first you can see her strech and yawn ( I imagine she just woke up ). After a few minutes we cleaned the litterbox and check her food and water she starts to become extremely active. And I mean extremely. I am not overreacting when I say she doesn't sit still for 5 seconds for at least 1 or 2 hours after we come home. Even if we ignore her for a minute she jump up and down the couch, the does random backflips, she attacks her toy for 2 seconds and the casually walks away. Sometimes she jumps like a rabbit, from the couch, to my belly on to my girlfirneds head, on to the table, all in 1 motion. 

Is this normal kitten behaviour? She has enough toys, we play with her as much as we can. Is she just more active then normal kittens or is this because she is bored? Or becasue she misses her litter ( its been 3 weeks by now ... )? Will she eventually calm down after sterilisation?

Thanks for the advice.