It is useful to consider the result for the energy eigenvalues for the one-dimensional box E_n = 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?