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Mathieu function. In mathematics, Mathieu functions, sometimes called angular Mathieu functions, are solutions of Mathieu's differential equation. where a, q are real -valued parameters. Since we may add π/2 to x to change the sign of q, it is a usual convention to set q ≥ 0.
The Mathieu equation is a linear second-order differential equation with periodic coefficients. For q = 0, it reduces to the well-known harmonic oscillator, a being the square of the frequency. The solution of the Mathieu equation is the elliptic-cylinder harmonic, known as Mathieu functions. They have long been applied on a broad scope of wave ...
Mathieu group. In group theory, a topic in abstract algebra, the Mathieu groups are the five sporadic simple groups M11, M12, M22, M23 and M24 introduced by Mathieu (1861, 1873). They are multiply transitive permutation groups on 11, 12, 22, 23 or 24 objects. They are the first sporadic groups to be discovered.
Gertrude Blanch. Gertrude Blanch (2 February 1897, in Kolno, Russian Empire (now Poland) – 1 January 1996) was an American mathematician who did pioneering work in numerical analysis and computation. She was a leader of the Mathematical Tables Project in New York from its beginning. She worked later as the assistant director and leader of the ...
Double-well potential. The so-called double-well potential is one of a number of quartic potentials of considerable interest in quantum mechanics, in quantum field theory and elsewhere for the exploration of various physical phenomena or mathematical properties since it permits in many cases explicit calculation without over-simplification.
The general solution of the above differential equation for a given value of a and q is a set of linearly independent Mathieu cosines and Mathieu sines, which are even and odd solutions respectively. In general, the Mathieu functions are aperiodic; however, for characteristic values of a n ( q ) , b n ( q ) {\displaystyle a_{n}(q),b_{n}(q ...
In mathematics, the Hill equation or Hill differential equation is the second-order linear ordinary differential equation. where is a periodic function with minimal period and average zero. By these we mean that for all. and. and if is a number with , the equation must fail for some . [1] It is named after George William Hill, who introduced it ...
Known for. Asymptotic expansions of Functions of mathematical physics and their eigenvalues, Quantum field theory, Periodic instantons, Supersymmetry. Scientific career. Fields. Theoretical Physics. Doctoral advisor. Robert Balson Dingle. Harald J.W. Mueller-Kirsten (born 1935) is a German theoretical physicist specializing in Theoretical ...