University Quantum Mechanics I · Finite Square Wells · 7.02
Classically forbidden regions and exponential decay
Where E < V the equation reads psi'' = κ² ψ with κ = √(2m(V0 - E))/ℏ, so ψ is a real exponential rather than an oscillation.
Course-map guide · not a complete lesson or simulationScope & orientation
What this subsection covers
Where E < V the equation reads psi'' = κ² ψ with κ = √(2m(V0 - E))/ℏ, so ψ is a real exponential rather than an oscillation.A strong response uses psi and |ψ|² with tails past the walls 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.
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.
Model, evidence, and boundary
What must be stated before selecting an equation for Classically forbidden regions and exponential decay?
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 must be stated before selecting an equation for Classically forbidden regions and exponential decay?
Quick check
Test the reasoning, not recall
What must be stated before selecting an equation for Classically forbidden regions and exponential decay?
Choose an answer to test the model.