As most of you know, according to the Player's Handbook, it isn't possible to cast a spell while wearing armor you aren't proficient in.
Have there been any rulings on this in regards to expending psionic focus, or using a psionic spell? Check this excerpt from Unearthed Arcana:
Psionics and Magic
Psionics and magic are two distinct forces. In general, an effect that affects a spell has no effect on a psionic effect. There is one important exception to this rule. A psionic effect that reproduces a spell is treated as magic. A psionic effect reproduces a spell when it allows a psionic creature or character to cast a spell. In this case, psionic energy taps into magic and manipulates it to cast the spell.
Best Answer
Yes, you can use any and all psionic abilities while wearing heavy armour. It's difficult to prove, but the article doesn't mention anything about armour constraining psionics. Similarly, the handy Sage Advice site built a collection of Mearls' tweets on psionics, and none of them mention anything, either.
Note that if you wear armour that you aren't proficient in, you will suffer the normal penalties of non-proficiency:
It's worth noting (on top of that first note), that this won't really affect your psionics at all, since the attack rolls you make with psionics are Intelligence-based, not Strength- or Dexterity- based.