# Some Write-Ups

These are some rather old write-ups of things which were once of interest to me...

Radiation Pressure Forces

This short document provides an overview of the current state of affairs concerning the forces excerpted by electromagnetic fields on spherical particles. 3 different methods are described (Radiative momentum balance, Maxwell-Stress-Tensor and the Dipole-Approximation + force density) and the Abraham-Minkowski controversy as well as the dispute between A. Rohrbach and P. C. Chaumet are reviewed.

Bernoulli Numbers, Riemann Zeta-function & Trigonometric Series Representations

Notes on the famous Bernoulli numbers... They appear in the series representations of several trigonometric functions. Also, a relation to the Riemann Zeta function for even integers is derived.

Curvilinear coordinates

Extensive notes and derived expressions for curvilinear coordinates

Sommerfeld Expansion

Details and calculations concerning the Sommefeld expansion encountered in solid state physics

Stirling's Approximation

Some notes on Stirlings' Approximation of n!

Moments of <r^n>(l,n) in quantum and classical mechanics.

This note derives a semi-classical expression for the expectation values of the moments of the radial coordinate, <r^n>, as a function of the angular momentum and principle quantum numbers l and n. The derivation starts with the time-average of the moment in Kepler orbits. A comparison to exact literature expressions is made.