Periodic potentials with minimal energy bands
Periodic potentials with minimal energy bands
We consider the problem of minimizing the width of the lowest band in the spectrum of Hill’s equation, <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="negative u plus q left-parenthesis x right-parenthesis u equals lamda u"> <mml:semantics> <mml:mrow> <mml:mo>−<!-- − --></mml:mo> <mml:mi>u</mml:mi> <mml:mo>+</mml:mo> <mml:mi>q</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mi>u</mml:mi> <mml:mo>=</mml:mo> <mml:mi>λ<!-- λ …