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We know that energy eigenvalues of a harmonic oscillator are En - (+) = hw Int When the system is in its ground state n = 0 and the corresponding energy is the zero-point energy. From the virial theorem (which applies to both quantum and classical harmonic oscillators), we know that the average kinetic and potential energies are equal, i.e., the total energy is equally partitioned among them. A) Show that you can express the expectation values of the kinetic and potential energy operators, T and V, using the knowledge of the corresponding variances (Ax)2 and (Ap)2 that read (4.x)2 = (22) (x)2 and (Ap)2 = (p2) (p)? Hint: think about what the expectation values of the position and momentum will be. B) Find the expression for the product of uncertainties AxAp for the nth state of the quantum harmonic oscillator. C) Does the uncertainty increase or decrease with increasing energy of the excitation level, i.e., with increasing n? Will the uncertainty obey the Heisenberg principle? Prove your statement mathematically. Comment on whether your conclusion holds true for the Morse potential