Objectives

• 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