An electron is confined to a one-dimensional box of length L.
(a) Sketch the wave function for the third excited state.
(b) What is the energy of the third excited state?
(c) The potential energy can't really be infinite outside of the box. Suppose that U (x) = + U0 outside the box, where U0 is large but finite. Sketch the wave function for the third excited state of the electron in the finite box.
(d) Is the energy of the third excited state for the finite box less than, greater than, or equal to the value calculated in part (b)? Explain your reasoning.
(e) Give a rough estimate of the number of bound states for the electron in the finite box in terms of L and U0.