University Quantum Mechanics I · The Free Particle · 5.02
Plane waves, and why no plane wave is a state
e(i(kx - ω t)) solves the equation, but |ψ|² = |A|² is constant, so the integral over all x diverges for every A other than zero.
Course-map guide · not a complete lesson or simulationScope & orientation
What this subsection covers
e(i(kx - ω t)) solves the equation, but |ψ|² = |A|² is constant, so the integral over all x diverges for every A other than zero.A strong response uses φ(k) beside the ψ(x) it builds 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
In a tank deep enough for kh >> 1, does a group of gravity waves travel at half the speed of the crests inside it, as ω = √(gk) requires?
Read the complete note
In a tank deep enough for kh >> 1, does a group of gravity waves travel at half the speed of the crests inside it, as ω = √(gk) requires? Useful evidence includes video tracking of one crest and of the group envelope, both speeds with uncertainty, their ratio against 1/2, and the two conditions checked explicitly: kh >> 1 needs water 15-25 cm deep with wavelengths of 5-15 cm (a paddle near 3-5 Hz), while wavelengths must stay well above the 1.7 cm gravity-capillary crossover, since below it surface tension takes over and vg exceeds vₚ instead..
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.
e(i(kx - ω t)) solves the equation, but |ψ|² = |A|² is constant, so the integral over all x diverges for every A other than zero. No choice of A repairs it: a plane wave is a limit of states, not one.
Model, evidence, and boundary
When should a model used for Plane waves, and why no plane wave is a state 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 Plane waves, and why no plane wave is a state be revised?
Quick check
Test the reasoning, not recall
When should a model used for Plane waves, and why no plane wave is a state be revised?
Choose an answer to test the model.