momentum at this point, so its momentum would not be continuous. Of course, in any realistic system, v does not have infinite jumps, so momentum will vary smoothly and thus d ' p/dx will be continuous d. How the energy levels grow with quantum number n as n- e. What the wave functions look like when plotted 2. You should go through the various wave functions treated in the Part 1(e.g, particles in boxes, rigid rotor, harmonic oscillator )and make sure you see how the probability plots of such functions are not at all like the classical probability distributions except when the quantum number is very large 3. You should make sure you understand how the time evolution of an eigenstate y produces a simple exp(i tE/-h)multiple of p so that p does not depend on time However, when p is not an eigenstate(e.g, when it is a combination of such states), its time propagation produces a p whose probability distribution changes with time 4. You should notice that the densities of states appropriate to the 1-, 2, and 3- dimensional particle in a box problem( which relate to translations in these dimensions) depend of different powers of E for the different dimensions 5. You should be able to solve 2x2 and 3x3 Huckel matrix eigenvalue problems both to obtain the orbital energies and the normalized eigenvectors. For practice, try to do so for2 momentum at this point, so its momentum would not be continuous. Of course, in any realistic system, V does not have infinite jumps, so momentum will vary smoothly and thus dY/dx will be continuous. d. How the energy levels grow with quantum number n as n2 . e. What the wave functions look like when plotted. 2. You should go through the various wave functions treated in the Part 1 (e.g., particles in boxes, rigid rotor, harmonic oscillator) and make sure you see how the |Y| 2 probability plots of such functions are not at all like the classical probability distributions except when the quantum number is very large. 3. You should make sure you understand how the time evolution of an eigenstate Y produces a simple exp(-i tE/ h) multiple of Y so that |Y| 2 does not depend on time. However, when Y is not an eigenstate (e.g., when it is a combination of such states), its time propagation produces a Y whose |Y| 2 probability distribution changes with time. 4. You should notice that the densities of states appropriate to the 1-, 2-, and 3- dimensional particle in a box problem (which relate to translations in these dimensions) depend of different powers of E for the different dimensions. 5. You should be able to solve 2x2 and 3x3 Hückel matrix eigenvalue problems both to obtain the orbital energies and the normalized eigenvectors. For practice, try to do so for