Objectives
Following your study of this chapter, you should be able to:
 explain the importance of the radial symmetry of the hydrogen atom potential (what does it allow us to do?)
 write down the Schrödinger equation in spherical coordinates
 follow the separation of variables of the Schrödinger equation to obtain a radial and an angular equation
 perform the derivation to find the ground state of hydrogen from the radial wave equation
 understand the purpose of spherical harmonics and state their general form
 state the names and the restrictions on the values of the quantum numbers n, l and ml
 know which quantum number quantizes angular momentum L, energy E and potential energy V
 state the equations for energy, magnitude of angular momentum and direction of angular momentum
 discuss the factors leading to the precession of m about the magnetic field
 explain how a magnetic field can remove a degeneracy of a given nl level and split spectral lines
 understand how the SternGerlach experiment provided evidence of space quantization
 write down the magnitude and the z component of the intrinsic spin angular momentum vector
 know the equation for the potential energy due to the spin magnetic moment
 describe the function of the gyromagnetic ratio and write down the equations for ml and ms
 summarize the selection rule for allowed transitions and show them in an energy level diagram
 calculate the most probable radius for an electron with a certain radial wave function
