A particle experiences a potential energy given by U(x) = (x2 - 3)e-x2 (in SI units), (a) Make a sketch of U(x), including numerical values at the minima and maxima; (b) What is the maximum energy the particle: could have and yet be bound? (c) What is the maximum energy the particle could have and yet be bound for a considerable length of time? (d) Is it possible for the particle to have an energy greater than that in part (c) and still be “bound” for some period of time? Explain.
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