University Quantum Mechanics I · Spin-½ · 13.04
The three Pauli matrices
σₓ = [[0,1],[1,0]], σy = [[0,-i],[i,0]], σz = [[1,0],[0,-1]]: Hermitian, traceless, each squaring to I, with σᵢ σⱼ = δᵢⱼ I + i epsᵢⱼₖ σₖ.
Course-map guide · not a complete lesson or simulationScope & orientation
What this subsection covers
σₓ = [[0,1],[1,0]], σy = [[0,-i],[i,0]], σz = [[1,0],[0,-1]]: Hermitian, traceless, each squaring to I, with σᵢ σⱼ = δᵢⱼ I + i epsᵢⱼₖ σₖ.A strong response uses transmitted fraction against analyser angle and states where the model stops being reliable.
Reasoning checklist
Evidence, assumptions and limits
Assumptions to state
State the system, observable, approximation, and conditions held fixed before using a model.
Evidence to collect
Does the resonance frequency of a DPPH sample scale linearly with applied field, and what g factor does the slope give against the free-electron value of 2.0023?
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Does the resonance frequency of a DPPH sample scale linearly with applied field, and what g factor does the slope give against the free-electron value of 2.0023? Useful evidence includes resonance frequency against Helmholtz-coil current with the field calibrated, a weighted linear fit, g with propagated uncertainty, the line width reported, and the limit stated: this fixes g, and takes s = 1/2 as given..
Limits to state
This GioPhysics course map is an adaptable learning sequence, not academic credit, accreditation, or a universal university syllabus.
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This GioPhysics course map is an adaptable learning sequence, not academic credit, accreditation, or a universal university syllabus. It is a first dedicated quantum-mechanics course, distinct from University Physics V, which covers quantum mechanics alongside atomic, nuclear and particle physics in twenty units: this course is narrower, slower, and teaches the linear algebra it needs rather than assuming it. Hydrogen appears here as an introduction, with the full radial derivation belonging to a second course. A midterm examination is assumed around week 8. Follow your institution's published scope, notation, laboratory programme, and assessment rules. A result should be checked against units, signs, limiting cases, and the conditions under which its model was derived.
Diagram & examples
Work the claim before choosing an equation
Interactive concept map
Follow the model from claim to evidence.
σₓ = [[0,1],[1,0]], σy = [[0,-i],[i,0]], σz = [[1,0],[0,-1]]: Hermitian, traceless, each squaring to I, with σᵢ σⱼ = δᵢⱼ I + i epsᵢⱼₖ σₖ. Those entries assume the z basis, and the set is special to spin-half.
Model, evidence, and boundary
Which response about The three Pauli matrices is most defensible?
modelModel, evidence, and boundary turns the stated idea into a representation that can make a prediction.
Example questions
Try the reasoning before revealing the structure.
Which response about The three Pauli matrices is most defensible?
Quick check
Test the reasoning, not recall
Which response about The three Pauli matrices is most defensible?
Choose an answer to test the model.