Category Archives: Physics

nutshell notes: free propagators

In section I.3 of QFT in a Nutshell, Zee examines the path integral for the Lagrangian \(\mathcal{L}(\phi) = \frac{1}{2}[(\partial \phi)^2-m^2\phi^2]\) (the “free”/”Gaussian” Lagrangian) with a source \(J\). This looks like $$\begin{align} Z(J)&=\int D\phi\,e^{i\int d^4x\,\{\frac{1}{2}[(\partial \phi)^2-m^2\phi^2]+J\phi\}}\\ &=\int D\phi\,e^{i\int d^4x\,\{-\frac{1}{2}\phi(\partial^2+m^2)\phi+J\phi\}}. \end{align}$$ (Integration by parts allows us to replace \((\partial\phi)^2\) with \(\phi(\partial^2\phi)\) in the exponent’s integrand.) The exponent [...]

timing planes with sound

If you’re standing outside and a plane passes overhead, it sounds like it’s coming from a bit further back than it looks like it’s coming from. This is because light travels practically instantaneously (c = 299,792,458 m/s = 670,616,629 mph, so you’re 0.00004 light-seconds from a plane 12000m in the air) while sound takes a [...]

all about: angular momentum in atoms

On my last test, I had trouble with a couple questions because I wasn’t totally clueful about how angular momentum works in atoms. I should fix this. Orbital angular momentum should come naturally: Our standard way of understanding electron states in atoms is with orbitals, which are chosen to have well-defined angular momentum quantum number [...]

all about: light-matter interaction

Or: “How photons and electrons say hello” Low energy — Photoelectric effect This is the first one you learn: a photon knocks an electron out of its atomic orbit. It is most likely to occur at low energies… as you move up in energy it becomes more likely that the photon will be scattered rather [...]

all about: splittings

So the electron in the hydrogen atom is just a particle in a spherically-symmetric 1/r potential… you’ve got a ladder of energy eigenvalues indexed by a quantum number n. The nth eigenvalue has degeneracy n2, but that’s cool; picking an axis z, the total angular momentum operator L and the z-axis angular momentum operator Lz [...]

things I really gotta work on

Having taken GRE Physics practice test 8677, it is clear that there are some very specific holes in my knowledge… Three main things: atomic physics (hydrogen atom: spectra? K series? Zeeman effect? Stark effect? selection rules? chemistry/orbitals?) nuclear physics (decay, what with \(\beta\)s and \(\alpha\)s and antineutrinos; binding energies) optics (diffraction, Rayleigh condition, indices of [...]