Technically, no. Potent Psionics requires you to "hit a creature with a weapon". An unarmed strike isn't a weapon, so you can't use Potent Psionics when you hit a creature with an unarmed strike.
However, unarmed strikes are melee weapon attacks. Given that Potent Psionics says:
At 8th level, you gain the ability to infuse your weapon attacks with psychic energy.
It's possible that it was intended to work with weapon attacks (which would include unarmed strikes) rather than with weapons specifically. As always with Unearthed Arcana, you have to remember the disclaimer:
These game mechanics are in draft form, usable in your campaign but not refined by design iterations or full game development and editing.
So while, technically, Potent Psionics doesn't work with unarmed strikes, you shouldn't be surprised if this changes in the final version of the Mystic.