Question

2. [10 points] For a Simple Harmonic Oscillator: a) Draw ψ(x) and ψ2(x) for the u, and v-6 states. Make sure to include as much detail as possible. b) Show that 2(3) is normalized. 3. [5] A certain non-halogen diatomic molecule was found to have a force constant of 99 N/m and an observed vibrational frequency of 162.2 cm1 Determine the identity of the unknown diatomic 4. [10 points) a) What is the difference between commuting and non-commuting operators? What is the physical manifestation of this? b) Provide AN example from our discussion in class of a commuting operator pair, and a non- commuting operator pair c) Using your selected commuting pair of operators, show that the following property is true: d) Of the following operators, which pair(s) commute? Justify your results by showing your work. A= B=x dx 5. [5 points] Determine if the following function f(x) is an eigenfunction of the operator G. If so, what is the eigenvalue? d2 dx2 6. [10] Considering the hydrogen atom: a) What are the normalization conditions for the hydrogenic wavefunctions? b) Set up the expression in as much detail as possible to show how you would confirm the orthogonality of the wavefunctions corresponding to any two of the 2p, 2py or 2p, states. You do not have to evaluate the expression.

Answer 1

2 Mug Muo_え