Consider a special case of eq. (8-5) in which each of the potentials V, V2 and V, are identical, in cach case of the form V(x) = 0 x>a and similarly for y and z. Use what you learned about the one-dimensional potential in Chapter 3 to find the eigenvalues and eigenfunctions for a particle in such a box.

Show explicitly that the alpha matrices are Hermitian. Do this in Dirac-Pauli representation.

Plot the first three wavefunctions and the first three energies for the particle in a box of length L and infinite potential outside the box. Do these for n = 1, n = 2, and n = 3

The essence of the statement of the uniqueness theorem is that if we know the conditions the limit that needs to be met by the potential of the system, then we find the solution of the system , then that solution is the only solution that exists and is not other solutions may be found. If we know potential solutions of a system, can we determine the type of system that generate this potential? If so, prove the statement! If no, give an example of a case that breaks the statement!