The third part in the video series explains two important topics in quantum mechanics. The first is Heisenberg’s uncertainty principle, that determines that it is impossible to fully discern simultaneously both the position and velocity of a particle. If we know the precise information of one, the uncertainty of the other increases (this principle can also be applied to pairs of other physical quantities). The second is the Schrödinger Equation, that provides the mathematical theory behind quantum mechanics.
This video regards several topics I would like to expand upon and possibly offer a slightly different point of view. First, regarding the meaning of wave functionality, or what is the wavelike description of particles. The wave function describes the probability of finding the position of a particle in space or in a certain velocity at a defined amount of time. In other words, it is the probability itself that presents a wavelike behaviour. When we take a measurement, a process called “wave function collapse” occurs. As we now know the position of the particle for certain, its wave function shifts and determines that it is indeed where we determined it is. However, a key fact to remember is that the position of the particle depended on the wave function prior to when the measurement took place.
The approach viewing particles as if they blink in and out of “existence” between different measuring points, is an approach I disagree with. In my opinion, the proper way to view this situation is that we do not know the location of the particle in between measurements. We can only know the wave function, meaning the probability of the particle to be in one place or another, but nothing more.
The second topic is the Schrödinger Equation, whose importance cannot be overestimated. The Schrödinger Equation depicts the entire quantum system, from the hydrogen atom, through the rest of the chemical elements and molecules including electrons within metals, electrons in semiconductors, superconductors and much more.
The solution to the Schrödinger Equation gives us a system of stable wave functions, meaning that if we use it on a system, the system will remain in this state until an external intervention changes its stability. In addition, the solution of the equation gives us the energy of the system in each of these conditions. (To the more advanced readers, I will note that this is an equation of eigenvalues of a matrix, or an operator called a Hamiltonian). For example, the solutions of the Schrödinger Equation in a hydrogen atom are the electron orbitals around the nucleus and the energy levels of each electron in such an orbital.
An interesting topic that the video only addresses briefly is the existence of virtual particles. Such particles are created for a short period of time from a vacuum and then disappear. In order for such a thing to occur, the created particles must abide by some condition. Can you figure out what this condition may be? If so, suggest your answer in response to this article, and I will let you know if you are correct.
Department of Condensed Matter Physics
Weizmann Institute of Science