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) ? 8 as x ? 8, its 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.
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