Parth G's video: Why Physicists Call This Equation the GOLDEN RULE of Physics

Get 5 days free and 20% off your annual Shortform membership here: https://www.shortform.com/parthg Fermi's Golden Rule is mathematical rule within the theory of quantum mechanics. It is used to calculate the transition probability between any two quantum states. In simpler terms, when we are studying systems with more than one possible state, like atoms which have multiple energy levels, then the Golden Rule formula can tell us how likely an electron is to transition from one state to another at any point in time. But the situation is a little bit more complicated than that. First, we see that a system's "allowed" energy levels can be calculated using the Schrodinger equation. This is done by inputting information about the system, such as its kinetic and potential energies, into the equation, and then solving for the "allowed" wave functions or eigenstates. These are the energy levels in which our system will be found whenever we make a measurement on it. For example, we will find each electron in one of the shells around the nucleus. However if the system is "perturbed" slightly, such as by a negatively charged electron passing relatively far away from the atom, then the allowed energy levels of the atom will also change. This is because the negatively charged electron will repel all the electrons in the atom, and attract all the protons in the nucleus. Thus, the potential energies we used to calculate the allowed energy levels of the atom will have changed, and hence the allowed energy levels themselves will have changed. When this is the case, however, the electrons in the atom are still in the "old" energy levels. And they will need to transition into the new energy levels. So which exact level will each electron transition into? Well, each electron could technically transition into any one of the new levels. However, there are two factors that affect the likelihood of a single electron to transition into a new state. Firstly, the "coupling" between the old state of an electron, and the new state we're studying. This is given by factors such as how close in energy the old and the new state are. The closer in energy, the strong the coupling, and the more likely our electron is to transition into this new state. Secondly, the transition probability also depends on the "density of states" around the new energy level. This means that states which are surrounded by other states very close in energy are more likely to receive the electron, because there are more states for the electron to transition into in the vicinity of that energy. Combining these two factors, we can figure out the probability per unit time that an electron will transition into a particular state. This is exactly what Fermi's Golden Rule studies and gives us a formula for. Thanks for watching, please do check out my links: MERCH - https://parth-gs-merch-stand.creator-spring.com/ INSTAGRAM - @parthvlogs PATREON - patreon.com/parthg MUSIC CHANNEL - Parth G's Shenanigans Here are some affiliate links for things I use! Quantum Physics Book I Enjoy: https://amzn.to/3sxLlgL My Camera: https://amzn.to/2SjZzWq ND Filter: https://amzn.to/3qoGwHk Timestamps: 0:00 - Energy Transitions and the Schrodinger Equation 2:42 - Big Thanks to Shortform for Sponsoring This Video! 4:39 - Changing the Energies in Our System 6:28 - Fermi's Golden Rule for Transitions This video was sponsored by Shortform