This Cheat Sheet is intended to supplement Quantum Physics For Dummies, 3rd edition, by Andrew Zimmerman Jones. It begins by reviewing some useful operators used in quantum mechanics calculations. Then it covers a useful method for solving the Schrödinger equation for the quantum wave function, and then how you can use that wave function to calculate probabilities in quantum physics.

At some point, your quantum physics instructor may want you to add time dependence and get a physical equation for a three-dimensional free particle problem. You can add time dependence to the solution forif you remember that, for a free particle,That equation gives you this form forBecausethe equation turns intoIn fact, now that the right side of the equation is in terms of the radius vector r, you can make the left side match:That’s the solution to the Schrödinger equation, but it’s unphysical.

At some point, your quantum physics instructor may want you to find the x, y, and z equations for three-dimensional free particle problems. Take a look at the x equation for the free particle,You can write its general solution aswhere Ay and Az are constants.Becauseyou get this forwhere A= Ax Ay Az.The part i

Each quantum state of the hydrogen atom is specified with three quantum numbers: n (the principal quantum number), l (the angular momentum quantum number of the electron), and m (the z component of the electron’s angular momentum,How many of these states have the same energy? In other words, what’s the energy degeneracy of the hydrogen atom in terms of the quantum numbers n, l, and m?

The photoelectric effect was one of many experimental results that made up a crisis for classical physics around the turn of the 20th century. It was also one of Einstein’s first successes, and it provides proof of the quantization of light. Here’s what happened. The photoelectric effect. When you shine light onto metal, as the figure above shows, you get emitted electrons.

Quantum physics, unlike classical physics, is completely nondeterministic. You can never know the precise position and momentum of a particle at any one time. You can give only probabilities for these linked measurements. In quantum physics, the state of a particle is described by a wave function, The wave function describes the de Broglie wave of a particle, giving its amplitude as a function of position and time.

The Schrödinger equation is one of the most basic formulas of quantum physics. With the Schrödinger equation, you can solve for the wave functions of particles, and that allows you to say everything you can about the particle — where it is, what its momentum is, and so on. In the following version of the Sch

Don’t think quantum physics is devoid of anything but dry science. The fact is that it’s full of relationships, they’re just commutation relationships — which are pretty dry science after all. In any case, among the angular momentum operators Lx, Ly, and Lz, are these commutation relations: All the orbital angular momentum operators, such as Lx, Ly, and Lz, have analogous spin operators: Sx, Sy, and Sz.