The purpose of this problem is to compare the time dependencies for systems in a superposition of two energy eigenstates in an infinite square well to those in a simple harmonic oscillator. Consider two systems (an infinite square well and a simple harmonic oscillator) that have the same value for their ground state energy Eground. 1) What is Ez, the energy of the 2nd excited state (the third lowest energy) of the infinite square well system in terms of Eground? Ez = Eground Submit 2) What is E3, the energy of the 2nd excited state (the third lowest energy) of the simple harmonic oscillator system in terms of Eground? Ez = Eground Submit 3) Now suppose the wave function for the infinite square well system is a superposition of two energy eigenstates, namely its ground state and its second excited state. Assuming Eground = 20 eV, what is ty, the minimum time it takes for the probability density plx, t) of the infinite square well system to return to its original value (p(x,0)) at t0? t = s Submit 4) Now suppose the wave function for the simple harmonic oscillator system is a superposition of two energy eigenstates, namely its ground state and its second excited state. Assuming Eground = 20 eV, what is ty, the minimum time it takes for the probability density p(x, t1) of the simple harmonic oscillator system to return to its original value (p(x,0)) at t = 0?