Problem 1 Hat\" Figure 1 shows a one-dimensional potential, known colloquially a

Question

Problem 1 Hat" Figure 1 shows a one-dimensional potential, known colloquially as the "Mexican potential. This potential has significant applications in real world physics: in condensed matter physics, it is used in phenomenological models of superconductivity, while in particle physics, it is the underlying potential of the Higgs Boson field that gives to all the particles in the universe. In this problem, you'll analyze the behavior for a classical model of this potential Take the form of the potential t be where r is the independent coordinate, and K and A are positive constants a. Determine the force, F(r) generated by this potential. Is this force conservative? b. Using the Newtonian formulation, determine the equation of motion for a particle of mass m in this potential The Mexican Hat poten 2000 Figure 1: The symmetric "Mexican Hat" potentials. The r and y axes are in arbitrary units.

Explanation / Answer

force is defind as the derivative of potential hence take the value f potential and solve for the value of force.

F=-dU/dx

F=kx-lambdax^3

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