No, the ME262 was the first (yes I know about the Gloster Meteor, it all comes down to the definition of operational) operational jet fighter of WWII and was powered by two Junkers Jumo 004 engines which were fairly horrible by modern standards. And standards then! As far as I know the T38 Talon is a jet trainer that dates from the early 60s with a GE engine that has no direct DNA with the Junkers Jumo.
R
I know this a really old thread but an interesting one.. Ron, the Gloster Meteor was operational in WWII from 1943, and never engaged in actual plane vs plane combat but what they did do rather well was to shoot down V1 flying bombs. I believe they accounted for several hundred before the launch sites were overrun in Holland..