In mathematics, the oscillator representation is a projective unitary representation of the symplectic group, first investigated by Irving Segal, David...

The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary smooth potential can usually...

controlled oscillator (NCO) is a digital signal generator which creates a synchronous (i.e., clocked), discrete-time, discrete-valued representation of a waveform...

realization was constructed by Gurevich-Hadani. Heisenberg group Oscillator representation Metaplectic structure Reductive dual pair Spin group, another...

unitary representations of locally compact topological groups. Oscillator representation Wigner–Weyl transform CCR and CAR algebras (for bosons and fermions...

roughly as the tensor product of the group ring of L with the oscillator representation in n dimensions (which is itself isomorphic to a polynomial ring...

over a maximal compact subgroup. Oscillator Oscillator representation orbit orbit method, an approach to representation theory that uses tools from symplectic...

applications in quantum mechanics, notably in the study of quantum harmonic oscillators and many-particle systems. An annihilation operator (usually denoted...

mechanics Kontsevich quantization formula Gabor–Wigner transform Oscillator representation Weyl, H. (1927). "Quantenmechanik und Gruppentheorie". Zeitschrift...

Drude particles are model oscillators used to simulate the effects of electronic polarizability in the context of a classical molecular mechanics force...

complex-valued function found to be the propagator of the quantum harmonic oscillator. It was first discovered by Mehler in 1866, and since then, as Einar Hille...

shares credit for what is often referred to as the Segal–Shale–Weil representation. Early in his career Segal became known for his developments in quantum...

Press (1966). Introduction to Superanalysis, Springer (1987). Oscillator representation Felix Berezin at the Mathematics Genealogy Project Yu. I. Manin;...

lattice. The ladder operators of the quantum harmonic oscillator or the "number representation" of second quantization are just special cases of this...

corresponding periodicity. The oscillator itself controls the phase with which the external power acts on it. Self-oscillators are therefore distinct from...

CPU is normally determined by the frequency of an oscillator crystal. Typically a crystal oscillator produces a fixed sine wave—the frequency reference...

of the phase noise of an oscillator, whereas digital-system engineers work with the jitter of a clock. An ideal oscillator would generate a pure sine...

harmonic oscillator, often described as a state that has dynamics most closely resembling the oscillatory behavior of a classical harmonic oscillator. It was...

devices. The timekeeping element in every modern clock is a harmonic oscillator, a physical object (resonator) that vibrates or oscillates at a particular...

strings. The TRNGs based on a free-running oscillator (FRO) typically utilize one or more ring oscillators (ROs), outputs of which are sampled using yet...

(2) 172 (2010), no. 2, 1407–1434. MR2680495 L-functions and the oscillator representation. Springer. 1987. ISBN 0691081565. with Stephen Gelbart and Ilya...

Nilpotent group Nilpotent Lie algebra Weil representation Theta representation Oscillator representation Weil, André. "Sur certains groupes d'opérateurs...

light modes, which are harmonic oscillators. Examples of Wigner-function time evolutions in a quantum harmonic oscillator Wigner quasiprobability distribution...

g(0) is a diagonal matrix with entries r, 0,...,0, where r > 1. Oscillator representation Symmetric cone See: Vinberg 1980 Paneitz 1983 See: Howe 1988 Folland...

frequency ν {\displaystyle \nu } (in the harmonic oscillator approximation). See quantum harmonic oscillator for graphs of the first 5 wave functions, which...

modeled as harmonic oscillators near their equilibria, a derivation of the resonant frequency for a driven, damped harmonic oscillator is shown. An RLC circuit...

of chronobiology (the study of circadian rhythms), the dual circadian oscillator model refers to a model of entrainment (where rhythmic events in an organism...

anharmonic oscillator): Sources of Quantum mechanics B.L. Van Der Waerden [2] The computations for the hydrogen atom in the Heisenberg representation originally...

Second quantization, also referred to as occupation number representation, is a formalism used to describe and analyze quantum many-body systems. In quantum...

power amplifiers in order to regulate power. On a voltage-controlled oscillator (VCO), such as in a radio transmitter, selection of the center frequency...