University Quantum Mechanics I · The Schrödinger Equation · 2.09
How boundary conditions quantise the energy
The ODE solves for every E; only isolated values leave a solution meeting both boundaries and staying normalisable.
Course-map guide · not a complete lesson or simulationScope & orientation
What this subsection covers
The ODE solves for every E; only isolated values leave a solution meeting both boundaries and staying normalisable.A strong response uses re ψ, im psi and |ψ|² on shared axes 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
Does a numerically evolved packet hold its norm constant, and does the probability lost from an interval match the current integrated through its two edges?
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Does a numerically evolved packet hold its norm constant, and does the probability lost from an interval match the current integrated through its two edges? Useful evidence includes ψ(x, t) from a stated integrator and grid, total norm against time, interval norm compared with the integrated flux at both edges, the drift traced to the time step, and the box edge named as the leak..
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.
The ODE solves for every E; only isolated values leave a solution meeting both boundaries and staying normalisable. ψ(0) = ψ(L) = 0 gives Eₙ = n² π² ℏ² / 2mL2. Only E below V's asymptotic value can be discrete.
Model, evidence, and boundary
When should a model used for How boundary conditions quantise the energy 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 How boundary conditions quantise the energy be revised?
Quick check
Test the reasoning, not recall
When should a model used for How boundary conditions quantise the energy be revised?
Choose an answer to test the model.