I'm a new H9 owner too but because mine shipped with a faulty power supply I'm well aware of its power requirements!
The supplied PSU is 9v, 500mA, tip positive. This polarity is the opposite of most effect pedals so DO NOT connect it to a third party power supply without first confirming that it can supply 500mA at 9v, and the tip (center) of the plug is positive, not negative.
Incidentally: With digital effects it's usually best to give them their own isolated power supply, otherwise you can get noise problems. I don't know if this is the case with the H9 (I'm a new user too) but it's common with digital effects.