Monthly Archives: April 2024
Wave Impedance
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
Legendre Transforms as Derivative Symmetrizers
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
Where Do Observables Come From?
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