Author Archives: wdengquantum.me

Consider an arbitrary worldline \(\{(t,\textbf x)\}\) of a classical system of particles in configuration spacetime. In general, this worldline need not correspond to any physical/on-shell trajectory; it can be as wildly off-shell as one likes, the only caveat being that … Continue reading →

Problem: What is the defining property of the (Cauchy) stress tensor (field) \(\sigma(\textbf x,t)\) of a material. Solution: The idea is that if one wants to find the stress vector (also called traction) \(\boldsymbol{\sigma}\) acting on a plane with unit … Continue reading →

Problem: To what kinds of waves does the concept of “wave impedance” \(Z\) apply to? Solution: (Transverse/longitudinal/dispersive/non-dispersive/plane/non-planar) travelling waves Problem: Why does it make more sense conceptually to consider the reciprocal of the impedance \(Y:=1/Z\) (called the admittance)? Solution: In … Continue reading →

Suppose you know that \(p\) is the derivative of some function with respect to \(v\). A natural question is whether or not the roles of \(v\) and \(p\) can be reversed, that is, can \(v\) also be viewed as the … Continue reading →

The purpose of this post is to explain where observables in non-relativistic quantum mechanics (notably the position \(\textbf X\), momentum \(\textbf P\), orbital angular momentum \(\textbf L\), spin angular momentum \(\textbf S\) and Hamiltonian \(H\) observables) arise from, and why … Continue reading →