Degeneracy: why n-squared states share one energy

Do the tabulated radial functions up to n = 3 normalise to one, and where does each radial probability density peak relative to the Bohr radius? Useful evidence includes normalisation integrals, radial probability curves for 1s, 2s and 2p, most probable and mean radii in units of a-nought, node counts checked against n minus l minus one, and the integration cutoff stated..

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.