Normalising psi and reading probabilities off it

For a set of candidate ψ(x), which admit a normalisation constant, what does that constant come to, and how does an interval probability move as the grid is refined? Useful evidence includes quadrature integrals of |ψ|² for Gaussian, triangular and 1/√(x)-tail trials, each constant against its analytic value, interval probabilities as the grid refines, and the 1/√(x) case shown to fail because |ψ|² falls only as 1/x and its integral diverges logarithmically.

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.