A typical quantum mechanics lecture contains a discussion of the WKB (or semiclassical) approximation. Within this framework, two results are usually derived:

1. WKB approximation for bound states (i.e. Griffiths Ch. 8.1)

2. WKB approximation for tunneling (i.e. Griffiths Ch 8.2)

For the latter case (2) I can think of very many cases where the WKB approximation may be useful even in current research. However, I am not really aware of any "real-life" applications of the WKB approximation (1) for calculating energies of bound states. Teaching this subject, I feel however that it would be more motivating for students to have such examples.

Does anyone know an interesting example, where the WKB approximation was used to calculate bound state energies? Preferably in a condensed matter context (but any other context is fine, too!), and maybe even from recent times (say last 30 years)?