2019/03/18 by Law, Chun-Kong, Luo, Yu-Chun, Wang, Tui-En
#34B45 #34L05 #82D25 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)
paper · doi:10.48550/arxiv.1903.07332
We study the spectrum of some periodic differential operators, in particular the periodic Schrödinger operator acting on infinite n-cubic graphs. Using Floquet-Bloch theory, we derive and analyze on the dispersion relations of the periodic quantum graph generated by 2-dimensional rectangles, and also n-cubes. Our proof is analytic. These dispersion relations define the spectra of the associated periodic operator, thus facilitating further analysis of the spectra.