Quantum Mechanics A Mathematical Introduction

In the previous chapter, we studied the consequences of rotations and angular momentum in three spatial dimensions, building up to the topic of this chapter: the quantum mechanics of the hydrogen atom. Hydrogen is, of course, the lightest element of the periodic table and consists of a proton and an electron bound through electromagnetism. Our goal for studying this problem is to determine the bound-state energy eigenstates, just like we did with the infinite square well and harmonic oscillator. These energy eigenstates will then tell us how the proton and electron are positioned with respect to one another in space, as well as the energy levels and how energy is transferred when the hydrogen atom transforms from one energy level to another. As always, our goal is to diagonalize the Hamiltonian Hˆ; that is, determine the states |ψ⟩ and energies E such that