Author Archives: anuj
Dirac’s Complex Momentum
Summary of the Paper In this pioneering paper, Dirac explores the mathematical and physical advantages of using complex variables in quantum mechanics. Traditional quantum theory relies on wave functions…Projection OPerators and Christoffel Symbols
Are Christoffel Symbols Related to Projection Operators? This is a deep and fascinating question — and it's insightful to sense a connection. While Christoffel symbols and projection operators arise in…
Parameterize a Curve
What Does It Mean: "Path Parametrized by \( \lambda \)"? A path parametrized by \( \lambda \) is a way of describing a curve through space by using a single…
Understanding Rindler Space
Understanding Rindler Space 1. What is Rindler Space? Rindler space describes the spacetime experienced by an observer undergoing constant acceleration in special relativity. It is useful for understanding: Uniformly accelerated…
Understanding the Event Horizon
Understanding the Event Horizon 1. The Event Horizon as a Global Concept The event horizon is not a physical surface but a mathematical boundary beyond which nothing can escape. Its…
Projection Operators and Symmetry
Projection Operators and Group Theory 1. How Projection Operators Relate to Group Theory Projection operators appear in quantum mechanics whenever we have symmetries described by a group \( G \).…
Gleason’s theorem with examples
Gleason’s Theorem Explained Using Single-Particle and Two-Particle Systems Read this post on Projection Operators first. 1. What Is Gleason’s Theorem? Gleason’s theorem states that in a Hilbert space of dimension…
Projection Operators along with examples. Gleason’s theorem next
Projection Operators and Measurement Outcomes Projection Operators and Measurement Outcomes 1. Single-Particle Spin Measurement Consider a quantum system where a spin-\( 1/2 \) particle (, an electron) is measured along…
Projection Operators and Gleason’s Theorem
Projection Operators and Gleason’s Theorem Projection Operators and Gleason’s Theorem 1. Projection Operators in Quantum Mechanics A projection operator \( P \) is a Hermitian operator satisfying: \( P^2 =…
Hannon’s Criticism of Einstein’s original derivation
Breakdown of Hannon’s Criticism of Einstein’s Derivation 1. Setup of Einstein’s Derivation Einstein considers two coordinate systems: Stationary system \( K \): Coordinates \( (x, y, z, t) \) Moving…