University Quantum Mechanics I · Measurement and the Uncertainty Principle · 4.02
Eigenvalue equations and determinate states
Q ψ = q ψ is the statement that every measurement of Q returns q: substitute it into σ-Q squared = ⟨(Q - q)²⟩ and the spread is zero.
Course-map guide · not a complete lesson or simulationScope & orientation
What this subsection covers
Q ψ = q ψ is the statement that every measurement of Q returns q: substitute it into σ-Q squared = ⟨(Q - q)²⟩ and the spread is zero.A strong response uses bar charts of |cₙ|² over a spectrum 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 momentum spread inferred from single-slit diffraction scale as 1/a, and does repeating one slit N times narrow the fitted width or only the error on its mean?
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Does the momentum spread inferred from single-slit diffraction scale as 1/a, and does repeating one slit N times narrow the fitted width or only the error on its mean? Useful evidence includes profiles at five slit widths, fitted angular half-widths, inferred Δ-p against ℏ / 2 Δ-x with the slit named as a state preparation rather than a disturbance, and N repeats on one slit showing the error on the mean fall as 1/root-N while the fitted width holds..
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.
Q ψ = q ψ is the statement that every measurement of Q returns q: substitute it into σ-Q squared = ⟨(Q - q)²⟩ and the spread is zero. Only normalisable eigenfunctions count as states, so no determinate state of x or p exists on the whole line.
Model, evidence, and boundary
What is the strongest test of a claim about Eigenvalue equations and determinate states?
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.
What is the strongest test of a claim about Eigenvalue equations and determinate states?
Quick check
Test the reasoning, not recall
What is the strongest test of a claim about Eigenvalue equations and determinate states?
Choose an answer to test the model.