Author Archives: anuj - Page 5
What replaces wave analytic continuity in the Matrix Mechanics picture?
In the schrodinger wave formulation of quantum mechanics, analytic continuity of the wave function plays an important part. What replaces analytic continuity when one switches to the Matrix formulation of…
Experimental Quantum Mechanics – wave versus matrix mechanics
The Two Pictures of Quantum Mechanics The wave picture and the matrix All the Useful Math Analytic continuation of wave funtions, analytic functions - all these conceptes developed over…
Poincare Recurrence Theorem – Mathematical
Poincaré Recurrence Theorem The Poincaré Recurrence Theorem is a foundational result in dynamical systems and ergodic theory, which asserts that a system in a finite phase space will, after sufficient…
Trajectories don’t exist
One of Heisenberg's greatest triumphs was simply eliminating the whole thought process around classical electron trajectories. He claimed that there are only observable quantities - and these quantities can be…
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…