CHEM 132B Study Guide - Quiz Guide: Spherical Harmonics, Position Operator, Electron Rest Mass
Document Summary
Consider the orthonormal set |pi, which are eigenfunctions of the linear momen- tum operator bp. State whether the following are true or false: the states |pi are eigenstates of the hamiltonian bh(x) with bv (x) = 0, the states |pi are eigenstates of the position operator bx. False: hp |bp2 |pi = 0 if p 6= p. true, hp| [bx,bp]|pi = 0. Consider the spherical harmonic functions yl,ml ( , ). State whether the follow- ing are true or false: the magnitude of the angular momentum of an orbital with y3,2 is 2 3 h. True: there are 2l + 1 nodes in for each l. false, the function y1, 1( , ) is orthogonal to all other spherical harmonic functions. True: the probability distribution of nding the electron within a given surface area a on the sphere ( , ) is p (r) = r2|rn,l|2. Molecular bond vibrations can be described well as quantum harmonic oscilla- tors.
