A particle with mass m moves in a potential U(x) = A |x|, where A is a positive constant. In a simplified picture, quarks have a potential energy of interaction of approximately this form, where x represents the separation between a pair of quarks. Because U(x) → ∞ as x → ∞, it's not possible to separate quarks from each other (a phenomenon called quark confinement).
(a) Classically, what is the force acting on this particle as a function of x?
(b) Using the uncertainty principle as in Problem 39.60, determine approximately the zero-point energy of the particle.