One-particle system Let be the [ Lagrangian ] for a system with time-varying position and velocity , with forces defined by a potential…
What are Hamiltonian dynamics? A system has [ phase space ] coordinates (p, q) , representing momenta and positions respectively. How do…
The Laplacian or Laplace operator computes the [ vector divergence ] of the gradient of a function , given by the sum of 'unmixed…
References: https://photonlines.substack.com/p/an-intuitive-guide-to-maxwells-equations Electric and magnetic fields : the electromagnetic…
Basic of quantum mechanics from Wikipedia : The quantum state of a system is a ray (equivalence class of vectors) in a separable (has a…
Measures uncertainty, disorder, or randomness. The (Shannon) entropy of a probability distribution is: The quantity inside the…
A macrostate in statistical mechanics is a collection of base-level states; equivalently, a subset of [ phase space ]. It's what you see…
Stack: goal: sample from conformations of arbitrary hydrocarbons (or whatever). simpler goal: sample from conformations of ethane. simpler…
Deriving here just for my own edification. At each timestep a rocket ejects mass at velocity relative to its current reference frame. At…
This post gives a nice, mathematically clear development of basic terms in statistical mechanics. Highlights: Think of a physical system as…
The divergence of a vector-valued function on a vector field measures the extent to which a given point is a source of the field. It…