The Hamiltonian operator

Do a clamped string's resonances sit at the eigenvalues of the same boundary-value problem that quantises a particle in a box, and where does the analogy fail? Useful evidence includes resonant frequencies against mode number with a linear fit and residuals, end correction and stiffness as systematics, and the disanalogy stated: one kₙ = n π / L feeds two different dispersion relations, so f goes as n here and E as n squared there..

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.