The Mathieu operator is the differential operator with cosine potential

Its eigenvalue equation is the Mathieu differential equation (Anahtarci and Djakov 2012, NIST DLMF). On the interval , the periodic conditions , and the antiperiodic conditions , give the two standard boundary value problems.

The almost Mathieu operator is a discrete cosine-potential counterpart, acting on doubly infinite sequences instead of functions of a continuous variable.

See also

Almost Mathieu Operator, Mathieu Differential Equation, Mathieu Function

Explore with Wolfram|Alpha

References

Anahtarci, B. and Djakov, P. "Refined Asymptotics of the Spectral Gap for the Mathieu Operator." J. Math. Anal. Appl. 396, 243-255, 2012. https://doi.org/10.1016/j.jmaa.2012.06.019.National Institute of Standards and Technology. "Definitions and Basic Properties." §28.2 in Digital Library of Mathematical Functions. https://dlmf.nist.gov/28.2.

Cite this as:

Weisstein, Eric W. "Mathieu Operator." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MathieuOperator.html

Subject classifications