Consider the infinite square well of width a. V(x) is infinite out side well and zero inside.
(a) Estimate the energies of the ground state as well as those of the first and the second excited states for (i) an electron enclosed in a well of size a = 10^-10 m (express your answer in electron volts); (ii) a 1g metallic sphere which is moving in a well of size a = 10 cm (express your answer in joules).
(b) Discuss the importance of the quantum effects for both of these systems.
(c) Use the uncertainty principle to estimate the velocities of the electron and the metallic sphere.