## 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 [...]

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 [...]