CHAPTER 4 - Hydrogen Atom

Abstract

The hydrogen atom has only one electron. The wave function ψ(r) of the electron in the hydrogen atom satisfies the Schrödinger equation. The hydrogen atom consists of a proton and an electron, and has a spherical symmetry that can most easily be studied using a spherical polar coordinate frame. Although the energy of an electron in a hydrogen atom can be specified by giving the quantum number n, the motion of an electron moving in three dimensions is not completely specified by giving the value of its energy. Levels of the hydrogen atom illustrate correspondence to definite values of n and l . For each choice of n and l, there are 2 l +1 values of m l and two values of m s . Each level corresponds to a total of 4 l + 2 different sets of quantum numbers. An energy level that corresponds to a number of independent states is said to be degenerate. Using this terminology, the energy levels of the hydrogen atom may be said to be (4 l + 2)-fold degenerate. The stationary states represent the possible ways the state of the hydrogen atom can evolve in a constant external field at a particular time t . The chapter also studies interaction of the hydrogen atom with an external magnetic Field.