Holy Quantized Mechanics Batman

Well Math is a lost cause at this point, there is no way that I am going to pass it anymore, so I think its time to tuck and roll away from wasting time on it.

In all its almost a good thing because Physics is starting to blow me away. We spent today working on the math and theory of the “Particle in a Box” system, which is a simple idealized system that can be completely solved within quantum mechanics. Wikipedia describes the system better than I can:

It is the situation of a particle confined within a finite region of space (the box) by an infinite potential that exists at the walls of the box. The particle experiences no forces while inside the box, but is constrained by the walls to remain in the box. This is similar to the situation of a gas confined in a container. …

As we shall see, the solution of the Schrödinger equation for the particle in a box problem reveals some decidedly quantum behavior of the particle that agrees with observation but contrasts sharply with the predictions of classical mechanics. This is a particularly useful illustration because this behavior is not “forced” on the system, it arises naturally from the initial conditions. It neatly demonstrates that quantum behaviour is a natural outcome of any wave-like system, contrary to the common concept of a “quantum leap” where the behavior is almost magical.

Easily the most mind-boggling feature of this model, is that experimentally and mathematically, if you placed a particle in the box, there is a chance that it can escape the box without having sufficient energy to escape though any classical means.