Vol 1 - L D Landau, E.M. Lifshitz - Mechanics · Problem 11.2

Collisions Between Particles

Physics — Landau & Lifshitz · period-of-oscillation-various-potentials

Problem

Determine the period of oscillation, as a function of the energy, when a particle of mass

m

moves in fields for which the potential energy is ((a))

U = A|x|^n

, ((b))

U = -U_0/\cosh^2 \alpha x

\quad -U_0 < E < 0

, ((c))

U = U_0 \tan^2 \alpha x