We found in the previous chapter that the molecular partition function is required to determine the thermodynamic properties of an ideal gas. To evaluate the partition function, specification of pertinent energy levels and degeneraciesis necessary. Such knowledge demands that we investigate at least the rudiments of quantum mechanics, and especially those quantum concepts required for subsequent applications to statistical thermodynamics. For this reason, we concentrate in the next few chapters on the Schr dinger wave equation, whose various solutions provide the ? _j s and g _j s needed for the eventual calculation of thermodynamic properties. Depending on your academic background, you might thus consider reviewing classical mechanics (Appendix G) and operator theory (Appendix H) in preparation for your upcoming study of quantum mechanics.

We begin this chapter with a historical review of the developments leading to the formulation of quantum mechanics, subsequently focusing on the Bohr model for atomic hydrogen and the de Broglie hypothesis for matter waves. We then introduce the Schr dinger wave equation, the basic postulates of quantum mechanics, and salient insights from these postulates germane to the development of statistical thermodynamics. We next apply the Schr dinger wave equation to the translation energy mode of an atom or molecule. This application conveniently explains both quantum states and quantum numbers, including their relation to our previous notions of microstate and macrostate. We end this chapter by...