University Quantum Mechanics I · Foundations of Quantum Mechanics · 1.02
Blackbody radiation and the Planck hypothesis
Counting cavity modes and giving each kT yields Rayleigh-Jeans and a divergence; restricting a mode to energies n h nu and summing a geometric series yields Planck's law, with h fixed by fitting radiance data.
Course-map guide · not a complete lesson or simulationScope & orientation
What this subsection covers
Counting cavity modes and giving each kT yields Rayleigh-Jeans and a divergence; restricting a mode to energies n h nu and summing a geometric series yields Planck's law, with h fixed by fitting radiance data.A strong response uses stopping potential against frequency, with slope h/e marked 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
For a set of candidate ψ(x), which admit a normalisation constant, what does that constant come to, and how does an interval probability move as the grid is refined?
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For a set of candidate ψ(x), which admit a normalisation constant, what does that constant come to, and how does an interval probability move as the grid is refined? Useful evidence includes quadrature integrals of |ψ|² for Gaussian, triangular and 1/√(x)-tail trials, each constant against its analytic value, interval probabilities as the grid refines, and the 1/√(x) case shown to fail because |ψ|² falls only as 1/x and its integral diverges logarithmically.
Limits to state
This GioPhysics course map is an adaptable learning sequence, not academic credit, accreditation, or a universal university syllabus.
Read the complete note
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.
Counting cavity modes and giving each kT yields Rayleigh-Jeans and a divergence; restricting a mode to energies n h nu and summing a geometric series yields Planck's law, with h fixed by fitting radiance data. Planck quantised the walls, not the field.
Model, evidence, and boundary
When should a model used for Blackbody radiation and the Planck hypothesis be revised?
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.
When should a model used for Blackbody radiation and the Planck hypothesis be revised?
Quick check
Test the reasoning, not recall
When should a model used for Blackbody radiation and the Planck hypothesis be revised?
Choose an answer to test the model.