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...

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

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

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

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

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...

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...

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

complex-valued function found to be the propagator of the quantum harmonic oscillator. Mehler (1866) defined a function E ( x , y ) = 1 1 − ρ 2 exp ⁡ ( − ρ...

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

Generally speaking, radio-frequency engineers speak of the phase noise of an oscillator, whereas digital-system engineers work with the jitter of a clock. Historically...

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

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

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

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

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

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

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

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...

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

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

state variables. Simple pendulum, see picture (right). Simple harmonic oscillator where the phase portrait is made up of ellipses centred at the origin...

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

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

each lattice vibrational mode is well described by a quantum harmonic oscillator. This approximation is implied in the parabolic shape of the potential...

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

described using a finite number of parameters Parametric oscillator, a harmonic oscillator whose parameters oscillate in time Parametric surface, a particular...

-dimensional isotropic harmonic oscillators. That is, each particle in our ensemble can be treated as a simple harmonic oscillator. The Hamiltonian for this...