Fourier decomposition: position space and momentum space

Does FFT evolution of a Gaussian packet, applying the free phase exp(−i ℏ k² t/(2m)) in k-space, reproduce σ₀ √(1 + (ℏ t/(2 m σ₀²))²), and where does the periodic grid break it? Useful evidence includes width fitted from |ψ|² at each step against the analytic curve, ⟨x⟩(t) against x₀ + ℏ k₀ t/m, the norm conserved to a stated tolerance, the time at which the packet reaches the grid edge and wraps, and one run started from a chirped packet that narrows before it spreads..

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.