Does anyone have this problem? You had enough sleep, but when you start your day you feel like you haven't slept at all. You feel tired and you feel bored easily, all you want is to rest.
In assumption you don't have any health issues first and foremost ask youself the following question.
Do you go to bed on regular hours? It's not all about how long you sleep but also if your sleeping schedule is more or less the same. If hours you go to bed are shifted daily for hour or two you may experience tiredness, being sort of out of phase.
If you want to check if this is the case conduct the following experiment: go to bed on preordained hour for at least 10 days. You should notice signifficant change and better regulation of your body day and night cycle. If this will not help, see a doctor.
Common things to consider: nutrition (supplements, perhaps) and diet (do you eat well? Do you eat a lot of carbohydrate heavy food? Are you eating something with protein in the morning), sleep routines, if you snore you could have sleep apnea (consult with a doctor: when I got a machine to feed me oxygen at night it turned my world around when I suffered from the same problem), exercise (are you getting any), meditation...
1) Try to eat your dinner at least 2 - 3 hours before sleeping. Avoid heavy food at dinner.
2) Highly recommended to switch off the laptop/PC and TV one hour before sleeping and try to read some relaxing book. I had tried this and found it to be very helpful.
3) As @Marcin pointed out I think it is very important to have a sleep routine. Sleep at almost same fixed time and wake up at almost the same fixed time.
4) Have you had a look upon your bed and pillow ? Is it comfortable and suited to your body ?
5) I do not wake up ultra fresh in the morning when the temperature of my room is not normal. The room temperature should not be too cold and not too hot. It should suite your body.
6) Take a hot water bath.
7) To be in the bed for very long at least in your scenario can also be very bad for your body. Try to go to bed when you are tired and ready to sleep.
8) The last thing I want to add: the best time according to me to sleep is from around 11 in the night to 6- 7 in the morning. I think sleeping well during the day makes my mood go down, makes the body lethargic, drowsy and it feels to me that I am not going through the day. The day is just passing by.
I have noticed this "problem" for me too, and I think one of the reasons is the interrupted sleep cycle (around 90 minutes, during the sleep we go through multiple such cycles).
I've recently started using http://sleepyti.me/ and it suggests the optimum hours of sleep (time of going to sleep and waking up time), that is based on the sleep cycles. I am noticing that this helps me getting better sleep even if I don't get to sleep much. Basically if you wake up in the middle of one cycle you are probably going to feel "worse" than if you wake up between cycles.
For an amazing read on sleep: http://supermemo.com/articles/sleep.htm