Abstract
Bloch waves are special solutions of Schrödinger's equation with a periodic real potential. They are plane waves multiplied by periodic functions. In this paper we prove the existence and completeness of Bloch waves and of the related Kohn-Luttinger waves in unbounded domains for a class of partial differential equations which includes the Schrödinger equation. In addition, we discuss the dependence of these waves and the corresponding eigenvalues on the wave vector of the associated plane wave. The results may be interpreted as the analogs for certain partial differential equations of Floquet's theory for ordinary differential equations or as the determination of the spectral representation of certain periodic Hamiltonian operators.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
