D&D 5E Converting Psionics to 5e?

[I'm A Banana]

Um...No! This is exactly why using an existing class is a horrible way to go, in my opinion. It feels nothing like mental powers in movies or books. To be honest, though, the only good mental power system that I have seen for any edition of D&D is Green Ronin's Psychic's Handbook.

Fair enough, it wasn't really designed with that in mind!

 

[aramis erak]

I kind of liked the 2E approach, myself. It doesn't work all that well in 3E or later...

But the casual psionic can be replicated with a variation on the apprentice feat, while an equivalent to a caster for a dedicated psion.

And I think that a sorcerer is a reasonable fit... just a different spell list. Given that the spell levels are essentially picked for balance levels, they are going to probably be the same. Psionics is no different from Arcane or Clerical magic in terms of overall power - it's just different in which spells appear on the list.

As for the "all the time" - give them a mastered spell much earlier than a wizard...