It is useful to consider the result for the energy eigenvalues for the one-dimensional box Eₙ=h² n² / 8 m a², n=1,2,3, ldots 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?
a) sqrt50, sqrt600, 1/20
b) 1/50, 1/600, sqrt1/20
c) 1/sqrt50, 1/sqrt600, 20