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First quantization information


First quantization is a procedure for converting equations of classical particle equations into quantum wave equations. The companion concept of second quantization converts classical field equations in to quantum field equations.[1]

However, this need not be the case. In particular, a fully quantum version of the theory can be created by interpreting the interacting fields and their associated potentials as operators of multiplication, provided the potential is written in the canonical coordinates that are compatible with the Euclidean coordinates of standard classical mechanics.[2] First quantization is appropriate for studying a single quantum-mechanical system (not to be confused with a single particle system, since a single quantum wave function describes the state of a single quantum system, which may have arbitrarily many complicated constituent parts, and whose evolution is given by just one uncoupled Schrödinger equation) being controlled by laboratory apparatuses that are governed by classical mechanics, for example an old fashion voltmeter (one devoid of modern semiconductor devices, which rely on quantum theory—however though this is sufficient, it is not necessary), a simple thermometer, a magnetic field generator, and so on.

  1. ^ Duck, Ian; Sudarshan, E C G (1998). Pauli and the Spin-Statistics Theorem. WORLD SCIENTIFIC. doi:10.1142/3457. ISBN 978-981-02-3114-9.
  2. ^ Dirac, P. A. M. (1950). "Generalized Hamiltonian Dynamics". Canadian Journal of Mathematics. 2: 129–148. doi:10.4153/cjm-1950-012-1. ISSN 0008-414X. S2CID 119748805.

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First quantization

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First quantization is a procedure for converting equations of classical particle equations into quantum wave equations. The companion concept of second...

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Canonical quantization

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In physics, canonical quantization is a procedure for quantizing a classical theory, while attempting to preserve the formal structure, such as symmetries...

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Second quantization

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Canonical quantization First quantization Geometric quantization Quantization (physics) Schrödinger functional Scalar field theory Second quantization on Wikiversity...

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Geometric quantization

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quantization is a mathematical approach to defining a quantum theory corresponding to a given classical theory. It attempts to carry out quantization...

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Quantum

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levels within an atom. Quantization is one of the foundations of the much broader physics of quantum mechanics. Quantization of energy and its influence...

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Color quantization

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In computer graphics, color quantization or color image quantization is quantization applied to color spaces; it is a process that reduces the number of...

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Old quantum theory

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orientations, so that the process of quantization does not pick out a preferred axis. For this reason, the name "space quantization" fell out of favor, and the...

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BRST quantization

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relatively rigorous mathematical approach to quantizing a field theory with a gauge symmetry. Quantization rules in earlier quantum field theory (QFT)...

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Quantization of the electromagnetic field

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function is derived from a "first" quantized Hamiltonian, the quantization of the Schrödinger field is the second time quantization is performed, hence the...

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Electromagnetic radiation

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sometimes known as the Planck–Einstein equation. In quantum theory (see first quantization) the energy of the photons is thus directly proportional to the frequency...

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Magnetic flux quantum

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from Φ0. The flux quantization is a key idea behind a SQUID, which is one of the most sensitive magnetometers available. Flux quantization also plays an important...

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Magnetic monopole

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charge quantization has appeared. (The concept of local gauge invariance—see Gauge theory—provides a natural explanation of charge quantization, without...

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Elementary charge

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the electric constant, and ħ is the reduced Planck constant. Charge quantization is the principle that the charge of any object is an integer multiple...

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Bohr model

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the quantized angular momentum condition of the Bohr model with an additional radial quantization condition, the Wilson–Sommerfeld quantization condition...

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Angular momentum operator

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{\displaystyle \hbar } is reduced Planck constant: A common way to derive the quantization rules above is the method of ladder operators. The ladder operators for...

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Kontsevich quantization formula

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deformation quantization of the corresponding Poisson algebra. It is due to Maxim Kontsevich. Given a Poisson algebra (A, {⋅, ⋅}), a deformation quantization is...

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Redshift quantization

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Redshift quantization, also referred to as redshift periodicity, redshift discretization, preferred redshifts and redshift-magnitude bands, is the hypothesis...

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Dither

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produce. Dither is added before any quantization or re-quantization process, in order to de-correlate the quantization noise from the input signal and to...

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Video codec

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the quantization stage. There, a best-effort approximation of inversion is performed. This part of the process is often called inverse quantization or...

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Audio bit depth

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determined by quantization error. The bit depth has no impact on the frequency response, which is constrained by the sample rate. Quantization error introduced...

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Time

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down in the figure depending on the acceleration of the observer. Time quantization is a hypothetical concept. In the modern established physical theories...

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Canonical quantum gravity

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canonical quantization techniques for constrained Hamiltonian systems invented by Paul Dirac.[3] Dirac's approach allows the quantization of systems...

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