Author Archives: anuj
Borel Algebras and Applications in Physics
Borel Algebra and Applications in Physics Borel Algebra and Applications in Physics Examples of Borel Algebras Real Line (\( \mathbb{R} \)): The Borel algebra on \( \mathbb{R} \) is generated…
Dipole Approximation in Electron-Photon Interaction
Dipole Approximation for Electron-Photon Interaction The dipole approximation assumes that the wavelength of the electromagnetic field is much larger than the spatial extent of the electron wavefunction. In this case,…
Electron interacts with a photon – Schrodinger equation and it’s solution
Schrödinger Equation for Electron-Photon Interaction The system includes: An electron with wavefunction ψe(r, t), A photon field described by the vector potential A(r, t). The total Hamiltonian includes: The electron's…
Analytic Functions on a Punctured Disk with Applications to Quantum Mechanics
Analytic Functions in Quantum Mechanics and Quantum Field Theory The following examples illustrate how different analytic functions defined on a punctured disk can be applied in quantum mechanics (QM) and…
Is ‘ Information ‘ subjective?
Does information has a subjective nature/aspect to it? Do we define something as being informative because we ourselves can perceive it? The perception can be either with lab instruments or…
Gödel’s Solution to Einstein’s Field Equations
Gödel's Solution to Einstein's Field Equations Kurt Gödel's solution to Einstein's field equations is a fascinating example of how general relativity (GR) can predict exotic spacetime geometries. Gödel introduced a…
Quantum Mechanics and the Transformation 1\(z-a)
Quantum Mechanics and the Transformation \( \frac{1}{z - a} \) Transformations of the form \( \frac{1}{z - a} \), especially in the context of complex analysis, appear in quantum mechanics,…
Richard Gott’s Three Universes at the Big Bang
Gott's Theory on the Big Bang Singularity J. Richard Gott, a Princeton physicist, proposed an intriguing theory concerning the Big Bang Singularity. His idea explores what happens if we consider…
Fault Tolerant, Error Correcting Computers for Quantum Computing
Fault Tolerant Computers for Quantum Computing Errors are part of the Quantum Computing equation. By 2035, IBM envisions fault tolerant computers, capable of breaking encryption algorithms. Quantum Safe Algorithms? There's…
Nowhere Differentiable Functions and Integration of such functions
Nowhere Differentiable Functions Nowhere differentiable functions are functions that are continuous everywhere but do not have a well-defined derivative at any point. They exhibit erratic behavior, and although they can…