Quantized systems

In the development of probability theory, as applied to a system of particles, it is necessary to specify the distribution of particles over die various energy levels of a system. The energy levels may be clearly separated in a quantized system or approach a continuum in the classical limit. The notion of probability is introduced with the aid of the general relation... 

In the electron-spin quantization system (x, y, z ), the quadrupole interaction matrix is ... 

The word LASER is an acronym for Light Amplification by Stimulated Emission of Radiation. The physical process upon which lasers depend, stimulated emission, was first elucidated by Einstein in 1917 (1). Einstein showed that in quantized systems three processes involving photons must exist absorption, spontaneous emission, and stimulated emission. These may be represented as follows ... 

Einstein s A and B coefficients. Quantized systems, such as atoms and molecules, emit and absorb radiation of frequency vy = E — Ej /hc in transitions between states i) and j) of energy , Ej. Einstein assumed that the probability that a system in state i) will absorb a photon of energy hcvij is proportional to the density of radiative energy per frequency interval, u(vij) dv. The probability of absorbing a photon in the time interval dt is given by... 

Here the ( ), denotes the expectation value of the quantized system in some suitable state [28,29]. 

None of the classically chaotic quantum systems so far investigated in the atomic and molecular physics literature exhibits type III quantum chaos. On the other hand, atomic and molecular physics systems provide excellent examples for quantized chaos, the topic of this section. The attractive feature of the term quantized chaos is that it does not imply anything about what happens to the classical chaos when it is quantized. Usually, especially in bounded time independent quantum systems, classical chaos does not survive the quantization process. The quantized system does not exhibit any instabilities, or sensitivity to initial conditions, e.g. sensitivity to small variations in the wave function at time t = 0. 

To emit energy from higher energy states, the temperature of a quantized system must be sufficiently high to excite those states. 

The modern student, to whom the Bohr frequency rule has become commonplace, might consider that this rule is clearly evident in the work of Planck and Einstein. This is not so, however the confusing identity of the mechanical frequencies of the harmonic oscillator (the only system discussed) and the frequency of the radiation absorbed and emitted by this quantized system delayed recognition of the fact that a fundamental violation of electromagnetic theory was imperative. 

The energy change of a quantized system is usually described in terms of ... 

Consider the notes that can be played on a piano. In what way is a piano an example of a quantized system In this analc, would a violin be continuous or quantized ... 

Because moments are extensive, non-local, objects, their use in quantizing the energy and wavefunction will implicitly be of a multiscale nature, proceeding from large through small scales, as more moments are used. In addition, since moments transform linearly under affine maps, any moment based analysis will incorporate some degree of space-scale invariance, which can be an efficient feature for quantizing systems. 

Zeigler, B. P. Lee, J. S. (1998). Theory of Quantized Systems Formal Basis for DEVS/ HLA Distributed Simulation Environment, in Aerospace/Defense Sensing and Controls. International Society for Optics and Photonics. 

A special generalized partition function, Q = igi c W was derived/discovered so that one can find the Boltzmann-weighted energy of a quantized system from the partition... 

S. Neretina, W. Qian, E. Dreaden, M.A. El-Sayed, R.A. Hughes, J.S. Preston, P. Mascher, Plasmon field effects on the nonradiative relaxation of hot electrons in an electronically quantized system. Nano Lett. 8,2410-2418 (2008)... 

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