Author Archives: anuj - Page 4
Momentum Space Representation of the 1\r Operator
Momentum Space Representation of the \( \frac{1}{r} \) Operator The operator \( \frac{1}{r}, \quad r = |\mathbf{x}| \) plays a central role in quantum mechanics, especially in Coulomb potentials,…
Estimate the nuclear radius size based on Electrostatic and Magnetic Field Strengths
The Rasetti–Fermi Paradox: Electrostatic vs. Magnetic Radius of the Nucleus The Rasetti–Fermi Paradox (1926–1927): Two “Radius” Estimates That Don’t Match A historical back-of-the-envelope puzzle: estimating a nuclear “radius” from an…
Time near the event horizon
Time Near a Black Hole’s Event Horizon Also read 'Tidal Forces inside a black hole' A clear relativistic description of what happens to time near the event horizon, seen from…
Tidal Forces inside a black hole
Tidal Forces for a 100 kg Human Falling into Black Holes Tidal Forces for a 100 kg Human Falling into Black Holes We quantify tidal accelerations for a 100 kg person of…
Boost of a Singlet Entangled State
Lorentz Boost of a Spin-Singlet: A Worked Example with Wigner Rotations Lorentz Boost of a Spin-Singlet: A Worked Example with Wigner Rotations We show explicitly how a Lorentz boost acts…
Entangled States and Reference Frames
Relativistic Treatment of Entangled Particles Also read - Boost of a singlet entangled state 1. Lorentz Invariance of Entanglement Entanglement is a property of the quantum state as a…
Fields of an accelerating charge
Electric Field of an Accelerating Electron For a point charge (electron) in motion, the electric field at an observation event can be decomposed into two parts: a velocity (near/Coulomb)…
Quantum Particle in an Accelerating Box
Quantum Particle in an Accelerating Box — How to Treat the Problem There isn’t a single “one-size” answer because what you do depends on how the box moves. 1) Box…
Historical Context of the Coupling Constant
Origin of the QED Coupling Constant The Coupling Constant in QED The QED coupling constant is one of the most famous “mystery numbers” in physics, better known as the fine-structure…
The Coupling Constant in QED
The Coupling Constant in QED The QED coupling constant is one of the most famous “mystery numbers” in physics, better known as the fine-structure constant, usually denoted: $$\alpha = \frac{e^2}{4…