It is useful to consider the result for the energy eigenvalues for the one-dimensional box En = h2n2/8ma2, n = 1, 2, 3, … as a function of n, m, and a.
a. By what factor do you need to change the box length to decrease the zero point energy by a factor of 50 for a fixed value of m?
b. By what factor would you have to change n for fixed values of a and m to increase the energy by a factor of 600?
c. By what factor would you have to increase a at constant n to have the zero point energies of a Ne atom be equal to the zero point energy of a hydrogen atom in the box?
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