Author Archives: anuj - Page 12
Free Scalar Field Equation – Solved using matrix mechanics
Free Scalar Field: Field Equation and Matrix Mechanics Solution Field Equation for a Free Scalar Field The action for a free scalar field φ(x) in four-dimensional spacetime is given by:…
Applying a conformal map to accomplish Block Encryption
Read First - Construct a conformal map Using Conformal Mapping in Block Encryption Conformal mappings preserve angles and local structures, making them conceptually relevant to cryptography. Here’s how the conformal…
Construct a conformal equivalence f between the “angle” {z ∈ C | z 6= 0, 0 < arg(z) < π/3} and the unit disk D ⊂ C
Constructing a Conformal Equivalence We aim to construct a conformal equivalence f between the "angle" A = { z ∈ ℂ | z ≠ 0, 0 < arg(z) < π/3…
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,…