Your perception of what a psychopath is colored by media portrayals and what notable psychopaths have done. Not all physicists are like Richard Feynman, and they're all at least reasonably smart.

What you're describing is a psychopath who is stupid. They do stupid things because they are stupid, and they do psychopath things because they're a psychopath. They aren't going to lead the police on a chase across the country after a string of murders. If they kill someone, they'll probably be caught the very first time. The reason they will kill will be somewhat less nuanced than an intelligent psychopath's reasons, but that's the smart vs. stupid difference - they're both psychopaths. Neither will feel remorse, neither will feel any compelling need to achieve their goals by not harming someone else, and both would do it again if they felt the circumstances warranted it. One will just do it in a way where he might not get caught and the other won't think that far ahead or will do such a poor job of it that thinking ahead won't help.