Summary on Special Relativity

I didn’t really understand the special relativity, although I get to know it for many years. But I know that I should make a summary of this fabulous theory when I came to be the TA for such kind of class.

Partition Function and Laplace Transform

Partition function is in fact the Laplace transformation of density of states.

Boltzmann Transport Equation

Before Maxwell and Gibbs introduced ensemble theory, physicists such as Bernoulli, Herapath, Joule, Kronig, Clausius, Boltzmann and so on has constructed the kinetic theory which is the beginnings of statistical mechanics. Kinetic theory starts with the microscopic movements of all of the particles, try to find out the distribution of these particles in space. Based […]

The Statistical Basis of Thermodynamics

How can we connect the macroscopic thermodynamics laws with the microscopic statistical dynamics? Here is the assumption, that the macroscopic state of a system has the largest possible number of microstates. Or in another way, every microstate of a closed system has the same probability, thus we can get the previous assumption.

Quantum Mechanics: Time-Dependent Perturbation Theory

1. Statement of the Problem The Hamiltonian we are considering is (1)   and we have already known the eigenkets and eigenvalues of (2)   What we are interested is that, If we are given an initial state (3)   what will it change with time? The Schrodinger Equation is (4)   Because the Hamiltonian […]

Differential Forms

The definition of Differential Forms Differential 1-forms A differential 1 form on a manifold is a sooth map (1)   of the tangent bundle of to the line, linear on each tangent space One could say that a differential 1-form on is an algebraic 1-form on which is “differentiable with respect to .” Also we […]

SI Units and Gauss Units

It happened many times that I cannot figure out which unit system I’m using in my derivation. Should I put a hare, or should I include a there? It seems that I need to make a conclusion for these two unit systems, this article is based on the appendix of Jackson’s Classical Electrodynamics.