Quadratic dispersion and why a free packet spreads

In a tank deep enough for kh >> 1, does a group of gravity waves travel at half the speed of the crests inside it, as ω = √(gk) requires? Useful evidence includes video tracking of one crest and of the group envelope, both speeds with uncertainty, their ratio against 1/2, and the two conditions checked explicitly: kh >> 1 needs water 15-25 cm deep with wavelengths of 5-15 cm (a paddle near 3-5 Hz), while wavelengths must stay well above the 1.7 cm gravity-capillary crossover, since below it surface tension takes over and v_g exceeds vₚ instead..

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.