That’s the thing that you square to get the probability of observing the system to be at the position x. So instead of, for example, a single position coordinate x and its momentum p, quantum mechanics deals with wave functions ψ( x). There are various ways of taking such a setup and “quantizing” it, but one way is to take the position variable and consider all possible ( normalized, complex-valued) functions of that variable. Those equations can be derived from a function called the Hamiltonian, which is basically the energy of the system as a function of positions and momenta the results are Hamilton’s equations, which are essentially a slick version of Newton’s original. By a “classical model” we mean something that obeys the basic Newtonian paradigm: there is some kind of generalized “position” variable, and also a corresponding “momentum” variable (how fast the position variable is changing), which together obey some deterministic equations of motion that can be solved once we are given initial data. Nature doesn’t work that way, but we’re not as smart as Nature is. may have originally wondered whether they were, but these days we certainly know better.Īs I remarked in my post about emergent space, we human beings tend to do quantum mechanics by starting with some classical model, and then “quantizing” it.
And sometimes people get brief introductions to things like the Dirac equation or the Klein-Gordon equation, and come away with the impression that they are somehow relativistic replacements for the Schrödinger equation, which they certainly are not. Not that the standard treatment of the Schrödinger equation is fundamentally wrong (as other aspects of how we teach QM are), but that it’s incomplete. Or, more accurately, I blame how we teach quantum mechanics. But one misconception came up that is probably worth correcting: people don’t appreciate how important and all-encompassing the Schrödinger equation is. Of course people chimed in with their own favorites, which is all in the spirit of the thing.
They represent a series of extraordinary insights in the development of physics, from the 1600’s to the present day.
Feel free to Google them for more info, even if equations aren’t your thing. In order: Newton’s Second Law of motion, the Euler-Lagrange equation, Maxwell’s equations in terms of differential forms, Boltzmann’s definition of entropy, the metric for Minkowski spacetime (special relativity), Einstein’s equation for spacetime curvature (general relativity), and the Schrödinger equation of quantum mechanics. Slightly cleaned up, the equations I chose as my seven favorites are: Part of the purpose of being on twitter is to one-up the competition, so I instead listed my #fav7equations. Over at the twitter dot com website, there has been a briefly-trending topic #fav7films, discussing your favorite seven films.