1. Last hour:
Generalized angular momentum EV’s: j·(j+1)·ħ2 for ; m·ħ for ; -j ≤ m ≤ j in steps of 1
The quantum numbers j can be integer or half-integer; j ≥ 0
can never point exactly along the z-axis, since
H atom Hamiltonian
Solutions have the form (r,,) = R(r)·Yℓm(,)
Radial Schrödinger equation:
New, “effective” potential

2. Solutions of the radial Schrödinger equation:
where
“associated Laguerre polynomials”

3. From Levine “Quantum Chemistry”

4. From Levine “Quantum Chemistry”

5. Learning Goals for Chapter 16 – The H-Atom
After this chapter, the related homework problems, and reading the relevant parts of the textbook, you should be able to:
explain the structure of the Hamiltonian of the H-atom;
explain the terms in the radial Schrödinger equation of the H-atom;
discuss the level structure of the H-atom and nodal structure of its eigenfunctions;
discuss the probability density of the H-atom;
calculate properties of the H-atoms for a given quantum state.