Rajesh Kumar

Dirac Oscillator

The Dirac oscillator is a relativistic quantum system that extends the Dirac equation by incorporating a linear dependence on both momentum and spatial coordinates.

Yang-Mills Theory

Following overview is based on youtube video Yang-Mills for Mathematicians by Sourav Chatterjee.

Degeneracy in Quantum Mechanics

Accidental degeneracy and other related degeneracies in quantum mechanics are discussed in the following papers.

PT symmetry is a concept in quantum mechanics that was introduced in the 1990s. It is based on the idea that the laws of physics should be invariant under the combined operations of parity (P) and time reversal (T). In other words, if a system is symmetric under the combined operations of parity and time reversal, it is said to exhibit PT symmetry.

Exceptional Orthogonal polynomials

Started with D G´omez-Ullate in 2004, the concept of Exceptional Orthogonal Polynomials (EOP) was introduced. This concept was further developed by C Quesne in 2008 and Yves Grandati in 2012.

Supersymmetry Quantum Mechanics

Started with L. Infeld, and T.E. Hull in 1951, the factorization method was used to solve the Schrödinger equation. This method was later used by Gendenshtein in 1983 to introduce the concept of shape invariance. This concept was further developed by Cooper and Freedman in 1983.