Excited states, half-wavelengths, and nodes

Does a two-term superposition oscillate at angular frequency (E₂ - E₁)/ℏ, and does a many-term packet return at the revival time 4mL²/(π ℏ)? Useful evidence includes snapshots of |Ψ(x, t)|², ⟨x⟩(t) with its fitted period set against 2 pi ℏ/(E₂ - E₁), |cₙ|² and ⟨H⟩ shown numerically constant, and the revival traced to level gaps that are integer multiples of E₁.

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.