Concluding Remarks and Research Outlook

It has been discussed and emphasized throughout this book that due to its very specific applicability conditions and the solution method itself, the WKB approximation is often employed in the situations where most of the other approximation methods are either unworkable or not efficient. In particular, we never needed to require that the internal interactions in our system should be negligible or even small. The WKB method could be applied to strongly correlated systems—a known obstacle for the density functional theory. The WKB approximation applies to dense quantum systems or to structures with highly nonuniform electron density, which are extremely difficult to approach using any other solution methods. All these circumstances make the WKB approximation a unique and unavoidable tool in investigating the electronic properties of various condensed matter systems, and I am strongly convinced that the WKB method will always be in demand and will find its new developments and applications in the recently discovered materials and nanoscale electronic devices.