BOOK: Quantum Mechanics, A Paradigms Approach, David H. McIntyre

CHAPTER: 5, 6 AND 9.

Do for x no, one obtains the energy eigenvalues of a particle conned to a box of length a [2. Region II (x) 32. Consider an innite square well potential with a delta function at x = (1/2 00 for x a V (x) = { V0ari[xa/2] for Osxsa Remembering the boundary conditions for a delta function (a) Find the wavefunction corresponding to even solutions about a f 2 when E > 0? (b) Find the energy levels corresponding to these even about solutions. The equation for the energy will be transcendental and therefore one must solve the equation numerically. Use two values for the dimensionless 2 where a has units of length and V0 has units of energy. constant, , equal to 0.5 and 2.0. It will be helpful to use a plot to indicate the location of the roots of the m a2 V0 equation. (c) Find the wavefunction corresponding to odd solutions about (1,12 when E > 0? Remember that an odd solution requires that the wavefunction must vanish at (1/2 . This modies the equations found for (a) and (b) and the solution reduces to that of the innite square well in which there is no delta function at the origin. (d) Find the energy levels corresponding to these odd solutions