Archives for Basic Quantum Theory - Page 3
Gamow’s Calculation of Alpha Decay – WKB Method
Alpha Decay Explained via Gamow and the WKB Method Alpha decay, the emission of a helium nucleus (\( \alpha \)-particle) from a heavy nucleus, was initially mysterious because classically…
Two particle wavefuction = 6 spatial dimensions
Why a Two-Particle Wavefunction Lives in Six Dimensions — and How That Gives Us Entanglement Ask a beginning student of quantum mechanics where a particle “is,” and they will…
No attributes even exist unless it is brought into interaction with a classical measuring device
John Bell’s Take on Measurement in Quantum Mechanics The claim that “for an atom, no attributes even exist unless it is brought into interaction with a classical measuring device” is…
Spin in Bohmian Quantum Mechanics
Electron Spin in Bohmian Mechanics Does Bohmian mechanics predict electron spin? No, Bohmian mechanics does not independently predict the existence of spin. Instead, it reproduces the predictions of standard…
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…