Quantum Mechanics Model Systems and the Hydrogen Atom

Chapter 10 introduced the basic postulates of quantum mechanics, illustrated key points, and applied the postulates to a simple ideal system, the particle-in-a-box. Although it is an ideally defined model system, the particle-in-a-box ideas are applicable to compounds having carbon-carbon double bonds like ethylene, and also to systems that have multiple conjugated double bonds, like butadiene, 1,3,5-hexatriene, and some dye molecules. The electrons in these systems do not act as perfect particles-in-a-box, but the model does a credible job of describing the energies in these molecules, certainly better than classical mechanics could describe them. Consider what quantum mechanics has provided so far a simple, approximate, yet applicable description of electrons in some tt bonds. This is more than anything classical mechanics provided. 

We will consider the following systems, the behavior of which have exact, analytic solutions for in the Schrodinger equation  

We will conclude this chapter with a discussion of the hydrogen atom. Recall that Bohr s theory described the hydrogen atom and correctly predicted its spectrum. TTowever, Bohr s theory was based on some assumptions that, when applied, provided the right answer. Quantum mechanics has its postulates, and we will see that it, too, predicts the same spectrum for the hydrogen atom. In order to be a superior theory, quantum mechanics must not only do the same things as earlier theories 

Unless otheiwise noted, all art on this page is Cengage Learning 2014 

---

Quantum Mechanics Model Systems and the Hydrogen Atom... 

---