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 Stern-Gerlach 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