CHEM 4502 Lecture Notes - Lecture 17: Spherical Harmonics, Legendre Polynomials, Rydberg Constant
Document Summary
We can solve schrodinger eq exactly for all one electron atoms (h or other atoms that have been ionized). Finally going to learn about origin of atomic orbitals! Previously discussed how bohr model of atom can successfully predict h emission spectrum and gave physical meaning to rydberg constant. But it"s wrong: incompatible w/ uncertainty principe, could not successfully be extended to systems w/ more than 1 electron, did not predict effects of magnetic fields on h atom. Our system consists of a proton and electron bound together. Center of mass motion (whole thing moves, translational motion) Wavefunction associated w/ center of mass = that for free particle which has mass equal to sum of masses of proton and electron. We"ll focus on motion w/in proton/electron system (not the above motion). As always, 1st step in solving schrodinger eqn is to determine hamiltonian for our system.
