Time evolution: two coupled ODEs and U(t) = exp(−iHt/ℏ)

Sweeping the detuning through zero at fixed coupling, is the minimum gap between the two eigenvalues equal to 2|V|, and does the population transfer match the Rabi formula at zero detuning and fall short of it away from zero? Useful evidence includes eigenvalues from numpy.linalg.eigh over a detuning sweep at several couplings, the minimum gap plotted against 2|V|, populations from exp(−iHt/ℏ) against the analytic Rabi curve at zero and at nonzero detuning, the norm tracked as a unitarity check, and the closed-system assumption named..

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.