University Quantum Mechanics I · Finite Square Wells · 7.04
Matching conditions: psi and psi' continuous at each wall
A finite step in V leaves psi and psi' both continuous at x = ±a; only an infinite step or a delta function breaks psi'.
Course-map guide · not a complete lesson or simulationScope & orientation
What this subsection covers
A finite step in V leaves psi and psi' both continuous at x = ±a; only an infinite step or a delta function breaks psi'.A strong response uses level ladders: finite well beside infinite 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
Beyond the critical angle, does the light crossing an air gap between two prisms fall off exponentially with gap width, and does the measured decay constant match the predicted kappa?
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Beyond the critical angle, does the light crossing an air gap between two prisms fall off exponentially with gap width, and does the measured decay constant match the predicted kappa? Useful evidence includes transmitted power against gap width, a log-linear fit whose slope is the power decay constant 2 kappa and must be halved before it is set against the field constant κ, that comparison made with the kappa predicted from incidence angle and refractive index, and the smallest trustworthy gap fixed by surface flatness..
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.
Model, evidence, and boundary
When should a model used for Matching conditions: psi and psi' continuous at each wall 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 Matching conditions: psi and psi' continuous at each wall be revised?
Quick check
Test the reasoning, not recall
When should a model used for Matching conditions: psi and psi' continuous at each wall be revised?
Choose an answer to test the model.