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University Quantum Mechanics I

University Quantum Mechanics I · Potential Barriers and Quantum Tunneling · 8.02

The potential step, above V0 and below it

One matching of psi and psi' at x = 0 gives r = (k1 - k2)/(k1 + k2) for both cases.

Course-map guide · not a complete lesson or simulation

Scope & orientation

What this subsection covers

One matching of psi and psi' at x = 0 gives r = (k1 - k2)/(k1 + k2) for both cases.

A strong response uses real and imaginary parts of psi across faces 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

Does microwave power crossing an air gap between two paraffin prisms fall exponentially with gap width, and does the fitted decay constant match the evanescent prediction?

Read the complete note

Does microwave power crossing an air gap between two paraffin prisms fall exponentially with gap width, and does the fitted decay constant match the evanescent prediction? Useful evidence includes transmitted power against gap width at fixed angle, a log-linear fit giving the decay constant with uncertainty, that constant against the value predicted from angle and index, standing waves named as a systematic, and a written statement that this is a classical electromagnetic analogue of barrier penetration - the same exponential mathematics, not a quantum measurement..

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 claimThe potential step, above V0 and below it

One matching of psi and psi' at x = 0 gives r = (k1 - k2)/(k1 + k2) for both cases.

Read the complete note

One matching of psi and psi' at x = 0 gives r = (k1 - k2)/(k1 + k2) for both cases. Above the step k2 is real and R is nonzero although the particle clears it, exactly as for waves at an impedance change. Below it k2 becomes i kappa with κ = √(2m(V0 - E))/ℏ, so |r| = 1, R = 1 exactly, and all that lies beyond is a decaying exp(−κ x) carrying no current. Penetration is not arrival, and no energy is borrowed to achieve it.

02 · RepresentationThe subsection's claim

Model, evidence, and boundary

03 · TestPrediction before measurement

What is the strongest test of a claim about The potential step, above V0 and below it?

04 · Evidence & boundaryDecide, then qualify

Does microwave power crossing an air gap between two paraffin prisms fall exponentially with gap width, and does the fitted decay constant match the evanescent prediction?

Read the complete note

Does microwave power crossing an air gap between two paraffin prisms fall exponentially with gap width, and does the fitted decay constant match the evanescent prediction? Useful evidence includes transmitted power against gap width at fixed angle, a log-linear fit giving the decay constant with uncertainty, that constant against the value predicted from angle and index, standing waves named as a systematic, and a written statement that this is a classical electromagnetic analogue of barrier penetration - the same exponential mathematics, not a quantum measurement..

Interactive diagram for The potential step, above V0 and below it: 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

What is the strongest test of a claim about The potential step, above V0 and below it?

Quick check

Test the reasoning, not recall

What is the strongest test of a claim about The potential step, above V0 and below it?

Choose an answer to test the model.