Bound states and what normalisability demands of the tails

Do graphical roots, a bracketed root-finder, and outward shooting return the same bound-state energies for one well, and where do they part? Useful evidence includes the z0 circle plot with its intersections read off, roots from a bracketed solver, eigenvalues from shooting, the three sets tabulated against the floor(2 z0/π) + 1 prediction, and the tolerance at which the methods disagree..

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.