How is it shown in the Schrodinger eqn that the success rate of tunneling increases as one's speed increases?

Question

hihi, i just read the book 'the physics of superheroes' and am rather interested with the physics of the Flash. Inside a chapter, it is mentioned that the speed of the Flash can be so fast, such that the probability of conducting quantum tunneling can become a certainty. However, i will like to ask how this is reflected in the Schrodinger equation. Can some1 explain it to me? Thank you very much... :)

Answer 1

It has been a long time since I dabbled in quantum mechanics, but - the faster Flash travels, the more energy he has available to get over the potential energy 'barrier' - the wave function representing his location broadens to extend beyond prohibited energy states (think of the wave function as his location probability) - the faster he goes the more smeared out his location probability is, so the probability of tunneling goes up. (regretably, he is so massive compared to electrons that we have done tunneling experiments with, that it would probably take the output of the sun to drive him to speeds where quantum tunneling was remotely probable..)
Shrodinger's equations describe the location probability of the particle wave function -