Notes Relativistic Hamiltonian for a charged particle The relativistic Hamiltonian for a charged particle in an external electromagnetic (EM) field can be derived from the relativistic Lagrangianwhere vector P = generalised momentum.The generalized …
Notes Equation of motion using Hamiltonian principle The equation of motion in covariant form can be obtained from the Lagragian by using Hamiltonian principleConsider the action integralIn order to write action in invariant form, we ...
Notes Thomas Fermi Method The Thomas-Fermi model is a semiclassical approach used in quantum mechanics to describe the electronic structure of atoms. It was developed independently by Llewellyn Thomas and Enrico Fermi in the …
Notes Normal Zeeman Effect and Anamolous Zeeman Effect The Zeeman effect refers to the splitting of spectral lines observed when the light emitted or absorbed by an atom is subjected to a magnetic field. The normal Zeeman effect ...
Notes Coulomb scattering cross section using Partial wave equation The Coulomb scattering cross section, often referred to as the Rutherford cross section, describes the likelihood of a charged particle undergoing a scattering event when interacting with the …
Notes Thomas-Fermi method The Thomas-Fermi method is an approximate quantum mechanical method used to describe the behaviour of a many-electron system, typically in atoms and solids. It was developed independently by …
Notes Degenerate perturbation theory Degenerate perturbation theory is a method used in quantum mechanics to analyze systems where the non-perturbed Hamiltonian operator has degenerate energy levels. In quantum mechanics, a degenerate …
Notes Vander Wall's Interaction Van der Waals interactions, often referred to as van der Waals forces, are a type of weak, non-covalent interaction that occurs between atoms and molecules. These forces play a crucial ...