In Breaking Bad, Walter White chooses to go by Heisenberg. I know that there has to be some significance behind both why Walt chose the name and why the writers chose that name as opposed to any other physicist's. It would make sense for it to have something to do with Heisenberg's uncertainty principle, which postulates (in broad strokes) that any system is fundamentally unstable on a short enough time frame. The connection between that and Walt's specific character eludes me though.
Because of the "uncertainty principle" which was created by the real Heisenberg and other similarities to Walter White.
As stated in this article
And also the cancer
If you think about when he first stated his name it was after his encounter with Tuco. At that point he is contrasting his old self to his new self meaning he knows his position, but not of his momentum. Or, he is uncertain of what his new momentum will do to his position. This is basically the uncertainty principle. This is also just my speculation.
Wikipedia for Uncertainty Principle by Heisenberg says that "the more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice-versa." Kind sums up the situation, nobody knew what Walter would do next and how he would do it. Also, he required to come up with a name when confronting Tuco for the first time and what better a name than Heisenberg.
Just to state some examples:
and a lot more situations where Walt just rocked!