The continuity equation and conservation of probability

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..

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.