Skip to main content
University Quantum Mechanics I

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 simulation

Scope & 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

01

Assumptions to state

State the system, observable, approximation, and conditions held fixed before using a model.

02

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?

Read the complete note

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..

03

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.

01 · Physical claimMatching 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'.

Read the complete note

A finite step in V leaves psi and psi' both continuous at x = ±a; only an infinite step or a delta function breaks psi'. Dividing one condition by the other gives the logarithmic derivative, which drops the unknown amplitudes and leaves one condition per wall: two equations for the interior amplitude ratio and for E.

02 · RepresentationThe subsection's claim

Model, evidence, and boundary

03 · TestPrediction before measurement

When should a model used for Matching conditions: psi and psi' continuous at each wall be revised?

04 · Evidence & boundaryDecide, then qualify

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?

Read the complete note

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..

Interactive diagram for Matching conditions: psi and psi' continuous at each wall: follow the physical claim through its representation, proposed test, evidence, and model boundary.

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.

Diagram check

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.