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In mathematics and physics, continuous spectrum is, roughly speaking, a non- countable set of eigenvalues of an operator. An operator acting on a Hilbert space is said to have a continuous spectrum if its eigenvalues can be changed continuously. If the spectrum of an operator is not continuous, we say that it is has discrete spectrum. Some of the basic questions in spectral theory are to characterise the discrete spectrum and purely continuous spectrum, just as a measure, such as a probability measure, can typically be split into 'atomic' and 'continuous distribution' parts

The position operator usually has a continuous spectrum, much like the momentum operator in an infinite space. But the momentum in a compact space, the angular momentum, and the Hamiltonian of various physical systems, specially bound states, tend to have a discrete (quantized) spectrum. It is the reason why quantum mechanicswavefunctions of an electron in a hydrogen atom possessing definite energy (increasing downward: n 1,2,3,. and angular momentum (increasing across: s p d . Brighter areas correspond to higher probability density for a position measurement. The angular mom was named in this way.

The quantum harmonic oscillatorThe quantum harmonic oscillator is the quantum mechanical analogue of the classical harmonic oscillator. It is one of the most important model systems in quantum mechanics because, as in classical mechanics, a wide variety of physical situations can be re or the Hydrogen atomA hydrogen atom is an atom of the element hydrogen. It is composed of a single negatively charged electron, moving around the positively charged proton which is the nucleus of the hydrogen atom. The electron is bound to the proton by the Coulomb force. are examples of physical systems in which the Hamiltonian has a discrete spectrum. In the case of the Hydrogen atom, it has both continuous as well as discrete part of the spectrum; the continuous part represents the ionized atom.

Functional analysisFunctional analysis Functional analysis is that branch of mathematics and specifically of analysis which is concerned with the study of spaces of functions. It has its historical roots in the study of transformations such as the Fourier transform and in t

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Topics: Continuous Spectrum, Continuous Game, Continuous Random Variable...

Continuous gameA continuous game or real-time game is a game without pauses, turns, rounds, or other stopping points. The term is most often used to describe video games, which as of the late 1990s were almost all real-time, the shift being driven by the rapid increase	Continuous random variableBy one convention, a random variable X is called continuous if its cumulative distribution function is continuous. That is equivalent to saying that Pr X a 0 for all real numbers a i. the probability that X attains the value a is zero, for any number a''.	Continuous functionIn mathematics, a continuous function is one in which arbitrarily small changes in the input produce arbitrarily small changes in the output. If small changes in the input can produce a broken jump in the changes of the output, the function is said to be
Continuous operationIn telecommunication, the term continuous operation has the following meanings: 1. Operation in which certain components, such as nodes, facilities, circuits, or equipment, are in an operational state at all times. Continuous operation usually requires th	Continuous Fourier transformIntegral transforms Unitary operators In mathematics, the continuous Fourier transform is a certain linear operator that maps functions to other functions. Loosely, the Fourier transform decomposes a function into a continuous spectrum of the frequencies	Continuous revelationIn general, continuous revelation or continuing revelation is a theological belief or position that God continues to reveal divine principles or commandments to humanity. Latter-day Saints In the Church of Jesus Christ of Latter-day Saints (LDS Church), c
Continuous wave	Continuous optimization	Continuous linear extension
Continuous positive airway pressure	Continuous time	Continuously variable transmission
Continuously variable slope delta modulation	Continuous wavelet transform	Continuous functional calculus

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