Quantum Physics: Expert Guides and Resources

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 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

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.

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?

In quantum physics, in order to find the first-order corrections to energy levels and wave functions of a perturbed system, En, you need to calculate E(1)n, as well as So how do you do that? You start with three perturbed equations: You then combine these three equations to get this jumbo equation: You can handle the jumbo equation by setting the coefficients of lambda on either side of the equal sign to each other.

Given that everything in quantum physics is done in terms of probabilities, making predictions becomes very important. And the biggest such prediction is the expectation value. The expectation value of an operator is the average value that you would measure if you performed the measurement many times. For example, the expectation value of the Hamiltonian operator is the average energy of the system you’re studying.

In quantum physics, in order to find the second-order corrections to energy levels and wave functions of a perturbed system, En, you need to calculate E(2)n, as well as So how do you do that? You start with three perturbed equations: You then combine these three equations to get this jumbo equation: From the jumbo equation, you can then find the second-order corrections to the energy levels and the wave functions.

In quantum physics, once you relate the angles of the scattered particles in the lab frame and the center-of-mass frame, you can translate the differential cross section — the bull's eye when you're aiming to scatter the particles at a particular angle — between the lab and center-of-mass frames. The differential area is infinitesimal in size, and it stays the same between the two frames.