Archives for Basic Quantum Theory
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…
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 =…
Projection Operators and Hidden Variables in QM
Gleason’s Theorem and Hidden Variables 1. Projection Operators A projection operator \( P \) is a Hermitian operator satisfying: P² = P These operators represent measurement outcomes in quantum…
Hidden Variables in Quantum Mechanics and Bell’s Rebuttal
Hidden Variables in Quantum Mechanics The Hidden Variables section in Ballentine's Statistical Interpretation of Quantum Mechanics examines the possibility of supplementing quantum mechanics with additional parameters (hidden variables) that determine…
Joint Probability Distributions in Ballentine’s Statistical Interpretation of Quantum Mechanics
Joint Probability Distributions in Quantum Mechanics Key Points: 1. Marginal Distributions Must Agree with Quantum Theory The joint probability distribution must reproduce the standard quantum probability distributions when integrated over…
Delta p = infinity does not mean momentum is infinite
Understanding Infinite Uncertainty in Momentum When Δp = ∞, it means that the uncertainty in momentum is infinitely large, not that the actual momentum itself is infinite. This distinction is…
Spin States are not a function of space
Spin Angular Momentum Definition For a spin-1/2 particle, spin operators are represented by the Pauli matrices: S_x = (ħ/2) σ_x, S_y = (ħ/2) σ_y, S_z = (ħ/2) σ_z where σ_x…