What is Quantization: Definition and 292 Discussions

Quantization, in mathematics and digital signal processing, is the process of mapping input values from a large set (often a continuous set) to output values in a (countable) smaller set, often with a finite number of elements. Rounding and truncation are typical examples of quantization processes. Quantization is involved to some degree in nearly all digital signal processing, as the process of representing a signal in digital form ordinarily involves rounding. Quantization also forms the core of essentially all lossy compression algorithms.
The difference between an input value and its quantized value (such as round-off error) is referred to as quantization error. A device or algorithmic function that performs quantization is called a quantizer. An analog-to-digital converter is an example of a quantizer.

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  1. M

    Canonical Quantization: Dirac's Book & Gauge Theories

    Hi, I have recently been reading Dirac's book on Canonical Quantization of gauge theories, and I have a few questions: So in the quantization procedure we need to identify all the constraints in the theory. Once this has been done (if we are dealing with a gauge theory) we need to check...
  2. A

    Sommerfeld quantization condition

    [b]1. The allowable radius of spinning electron in uniform magnetic field using sommerfield quantization condition [b]3. Subs mv/r=qvB and some of its variation (like th period 2pi*r /v) into the closed int of pdq=nh and I got r=sqr((nh)/(2pi*qB)). Is this correct. I can't find anything about...
  3. Q

    What is responsible for quantization?

    I'm reviewing my undergraduate quantum mechanics from a while back, and I am not quite sure I understand this correctly. I seem to recall being taught that quantization arises from the imposition of boundary conditions (in the mathematical sense). But this isn't quite the same as saying that...
  4. A

    Operator in second quantization

    Hello, I'm struggling with the second quantization formalism. I'd like to derive the hamiltonian of a system with non-interacting particles \hat{H}=\int dx\,a(x)^\dagger \left[\frac{\hat{P}}{2m}+V(x)\right]a(x), where a(x) = \hat{\Psi}(x). I know the second quantized representation of a...
  5. J

    Faraday's Law and Charge Quantization

    Homework Statement My textbook indicates the following three important points are confirmed by Faraday's law of electolysis: a) matter consists of molecules and molecules consist of atoms b) charge is quantized; only integral numbers of charges are transferred to the electrodes c)...
  6. D

    Second Quantization: Wave Function & Creation/Annihilation Operators

    Hi. In second quantization (not QFT or anything advanced like that) we have the particle density \hat n(x)=\Psi^{\dagger}(x)\Psi(x) using the usual field creation/annihilation operators. For a single particle we obtain for the expectation value in the state |\psi\rangle: \langle \psi |...
  7. tom.stoer

    (canonical) quantization of teleparallel gravity

    Does anybody know about an attempt to quantize teleparallel gravity? I would like to learn more about it, canonical approaches preferred: is there a sound formalism to implement the constraints / symmetries? Do we know the physical Hilbert space? Can one construct Dirac observables? Does the...
  8. I_am_learning

    What does space quantization of angular momentum actually signify?

    I have just come to learn (Physics, with modern physics, Richard Wolfson, J M. Pasachoff, second edition) that not only angular momentum's magnitude is quantized, but also its direction. Its given that, Cos\thetamin= l / \sqrt{l(l+1)} Telling that, \thetamin is the minimum angle between any...
  9. P

    What is Macroscopic Quantization and How Does it Affect Everyday Objects?

    I'm learning about Schrodinger's equation in my general chem class right now, so obviously I'm doing a little background reading on quantum theory. The following is an excerpt from a supplement on basic (very basic) quantum theory: The answer is that quantization is only noticeable when...
  10. maverick280857

    Functional Quantization of Scalar Fields

    Hi everyone, I'm reading section 9.2 of Peskin and Schroeder, and have trouble understanding the origin of a term in the transition from equation 9.26 to 9.27. Specifically, equation 9.26 is \frac{1}{V^2}\sum_{m,l}e^{-(k_m\cdot x_1 + k_l\cdot x_2)}\left(\prod_{k_{n}^{0}>0}\int d \Re...
  11. P

    Representation of second quantization

    In coordinate representation in QM probality density is: \rho(\vec{r})=\psi^*(\vec{r})\psi(\vec{r}) in RSQ representation operator of density of particles is \hat{n}(\vec{r})=\hat{\psi}^{\dagger}(\vec{r})\hat{\psi}(\vec{r}) Is this some relation between this operator and density...
  12. W

    Energy quantization of oscillator

    Homework Statement A simple pendulum has a length equal to 0.6 m and has a bob that has a mass equal to 0.5 kg. The energy of this oscillator is quantized, and the allowed values of energy are given by En = (n + 1/2)hf0, where n is an integer and f0 is the frequency of the pendulum. Find n if...
  13. A

    Path Intergral quantization for Relativistic Point like particle?

    Dear all, Since standard QM textbook Sakurai or Shankar only mention Non-relativistic path integral and QFT text deal with path integral for field theory, I want to ask whether there is a subject like "Path Intergral quantization for Relativistic point like Particles"? If so, is this subject...
  14. S

    Energy quantization in schrodinger equation

    in schrodinger equation(time independent) d^2y/dx2= 2m/h^2(V-E)y, V is a function of position coordinate, y is eigenfunction. if E>V , y being -ve or +ve it would be a oscillatory function. The allowed energy values are continously distributed...
  15. T

    Wilson-Sommerfeld quantization rules

    Homework Statement Use the Wilson-Sommerfeld quantization rules to obtain the energy levels of a perfectly elastic particle of mass m in a cubic box of edge a in terms of the quantum numbers n_x, n_y, n_z Homework Equations \oint pdq = nh Where p is a momentum, and dq is the corresponding...
  16. G

    Second quantization of field operators

    Homework Statement (from "Advanced Quantum Mechanics", by Franz Schwabl) Show, by verifying the relation \[n(\bold{x})|\phi\rangle = \delta(\bold{x}-\bold{x'})|\phi\rangle\], that the state \[|\phi\rangle = \psi^\dagger(\bold{x'})|0\rangle\] (\[|0\rangle =\]vacuum state) describes a...
  17. N

    How Does Quantum Mechanics Explain Nearly Equal Energy States in Ammonia?

    Homework Statement In a streamlined model for the low energy states of an ammonia atom, (NH3), imagine that a nitrogen atom moves in one dimension in the potential V(x) sketched in figure I.1(found in Peebles textbook on p.86); The potential has two minima, one on each side of the triangle...
  18. M

    Bohr's Quantization of Angular Momentum

    Bohr's second postulate says that it is only possible for an electron to move in an orbit for which its orbital angular momentum L is an integral multiple of \hbar. Can somebody please derive and explain L= n\hbar for me? I feel like a total dummy for not understanding this, but this is what I...
  19. E

    Photon wavelength quantization?

    Are photon wavelengths quantizised? If so, what are their possible wavelengths? Do their possible wavelengths also depend on the system they are in?
  20. M

    What is the essence of quantization?

    How should I understand the procedure of canonical quantization in quantum field theory. Do we really quantize the field by regarding the field as dynamics variables ?What’s the physical essence of quantization?
  21. J

    Why fundamental quantization of energy is hv?

    Now this might seem to be a very stupid question. But neverthless, I don't understand why the fundamental quantization of energy must be hv? why not any value lower or higher like hv^2 or h/v^2. Is it possible to prove that this value of quantization is most favourable than any other value...
  22. A

    Quantization of Orbits: Explained

    hi there we know that electrons around the nucleus in an atom can only exist in certain discrete energy levels (orbits) and that they can jump from one energy state to a higher one or a lower one. where is the electron when it is jumping from a higher stste to a lower state if it cannot exist...
  23. L

    Second quantization and partial traces

    Hi! Is there a common way to write a fermionic Fock space (finite dimensional) as a tensor product such that it is possible to do a partial trace over one particle type? Sorry, if this is an obvious question, but I just can't see it. Thanks!
  24. MTd2

    Path Integral Quantization in Finsler Geometry

    http://arxiv.org/abs/0904.2464 Finsler Geometrical Path Integral Authors: Takayoshi Ootsuka, Erico Tanaka (Submitted on 16 Apr 2009) Abstract: A new definition for the path integral is proposed in terms of Finsler geometry. The conventional Feynman's scheme for quantisation by...
  25. T

    Question about spacetime quantization

    I have a question about spacetime...if spacetime was quantized, would we still be considered to have 3 spatial dimensions? As far as I understand, 3 numbers are the minimum that we currently need to specify a location somewhere in space after selecting an arbitrary origin (the numbers are...
  26. marcus

    Current BH-LQG topics (e.g. quantization of entropy)

    Here are the talks planned for this month's BH-LQG workshop. I think one thing that motivated the organizers is the recent appearance of results showing a step-wise increase in BH entropy. That is the increase is only approximately linear with horizon area---detailed analysis shows more...
  27. L

    The meaning of time in curved space quantization

    in diffeomorphism invariant theory, which is the meaning of the time in quantization? or in other words which is the right time for quantization?
  28. N

    Can the Pauli Exclusion Principle explain the quantization of the nucleus?

    My professor mentioned that the pauli exclusion principle applies to the nucleus. How exactly is the nucleus quantized (the protons and neutrons), and how do the quantization rules apply to it (such as pauli's, hunds, and so on). Also, is this the reason why we don't observed multiple neutrons...
  29. S

    Are Quasars and Galaxies Redshifts Truly Quantized?

    http://arxiv.org/PS_cache/arxiv/pdf/0712/0712.3833v2.pdf Fourier spectral analysis has been carried out on the quasar number count as a function of redshift calculated from the quasar data of the Sloan Digital Sky Survey DR6 data release. The results indicate that quasars have preferred...
  30. L

    Second quantization in ashtekar variable

    I am searching material in second quantization in ashtekar-like formulation gravity. Somebody knows something like that? thanks
  31. M

    Quantization using the bohr model

    bohr model: permitted radii? Homework Statement A new (fifth) force has been proposed that binds an object to a central body through a potential energy function given by: U(r) = -Dr^{\frac{-3}{2}} 2 r > 0 and D > 0 (a) What is the (central) force F(r) associated with this potential...
  32. M

    Question about quantization of scalar field

    Why the quantization of scalar field resolves the energy negative problem that exist in the klein-gordon equation?
  33. L

    Where can I find detailed description of cononical quantization?

    For example, I want to know how to quantize a free particle in the spherical coordinates. Given a classical Hamiltonian H(r, \theta, \phi, p_r, p_{\theta}, p_{\phi}), the standard procedure tells us to let r, \theta, \phi be operators and they form a complete set. And The corresponding...
  34. thenewmans

    Quantization of Color: Electrons Jump Between Orbits

    Is there any paper on the quantization of color? Maybe not since it’s obvious. I always thought that color was on a continuum. But now I realize that electrons jump between a limited set of orbits.
  35. F

    Cosmology and Energy Quantization in Matter

    Quantum Wave Cosmology is a niche in cosmology that consists of a group of “not easily refuted” protoscience ideas about a universe composed of nothing but energy. A few QWC ideas include: The universe is composed of one commodity, energy. Energy cannot be created or destroyed and so...
  36. F

    Cooper pairs - 2nd quantization

    Hi all, I am looking at (elementary) theory of superconductivity. In particular, I am looking at the calculation showing that a (however small) attractive interaction makes the Fermi sea unstable. Kittel's "Introduction to solid state physics" (7 ed) sketches this calculation in Appendix...
  37. W

    The necessity of the 2nd quantization?

    Is the 2nd quantization physically essential in the description of relativistic fermions obeying Dirac equation? In the case of the non-relativistic Schrodinger equation, the 2nd quantization is only a matter of convenience and doesn't actually change any physics, for both bosons and...
  38. M

    Canonical quantization with constraints

    let be the Lagrangian (1/2)m( \dot x ^{2} + \dot y^{2}) - \lambda (x^{2}+y^{2}-R^{2}) with 'lambda' a Lagrange multiplier , and 'R' is the radius of an sphere. basically , this would be the movement of a particle in 2-d with the constraint that the particle must move on an sphere of...
  39. Q

    Schrodinger Equation and Energy Quantization

    I'm a bit embarrased to ask this (thats why I'm asking here and not asking one of my professors), as a grad student in Physics I've had a good deal of quantum mechanics, but one thing I haven't fully understood yet is the mechanism in the Schrodinger Equation that forces eigenvalue quantization...
  40. M

    Quantization of Gauge theories ?

    Quantization of Gauge theories ?? Hi , i am trying to learn the math formalism of Gauge Theories as far as i know they begin with the 1-form A= \sum_{i} T^{i}A_{\mu}^{i} where 'T_i ' are the generators of the Lie Group then we define the 2-form F= dA + (1/2)[A,A] and the...
  41. J

    Quantization of relativistic point particle, string style

    I don't have the Zwiebach's string theory book myself, but I paid a visit to a library, and took a glance on it. The chapter 5 was about relativistic point particle. Now, did I understand correctly, that the string people actually have a technique to quantize a relativistic point particle? I...
  42. C

    Spinfoams as a form of quantization?

    So this is sort of a belated response to some comments that were made in here over the last couple weeks and that I've been thinking about since. In the thread about the Lisi article in the New Yorker, Mtd2 and Kea were asking Garrett about whether he is still using a "superconnection" and...
  43. A

    Anderson Hamiltonian (product of number operators) in 1st quantization?

    In the Anderson model, it cost an energy Un_{\Uparrow}n_{\Downarrow} for a quantum dot level to be occupied by two electrons. Here n_{\Uparrow} is the second quantized number operator, counting the number of particles with spin \Uparrow. I need the term Un_{\Uparrow}n_{\Downarrow} in first...
  44. P

    Uniqueness of quantization of Dirac field

    Let's have a theory involving Dirac field \psi. This theory is decribed by some Lagrangian density \mathcal{L}(\psi,\partial_\mu\psi). Taking \psi as the canonical dynamical variable, its conjugate momentum is defined as \pi=\frac{\partial\mathcal{L}}{\partial(\partial_0\psi)} Than the...
  45. A

    Books that cover Second Quantization?

    So I actually decided to make an effort to study for my quantum final ahead of time, and I'm trying to find books that cover second quantization. If possible I'd like to find a book that gives a decent explanation (with examples, maybe?) of the Bogoliubov transformation. Does anyone have any...
  46. A

    Exploring Flux and Voltage Quantization in Superconductors: A QM Perspective

    I have read that when the rate in change in flux wrt time=0 the current become constant and the flux get trapped in the superconductor loop but how does this flux quantization exist exactly and under which rules it exist? and i want to ask is there something called voltage quantization?! and if...
  47. N

    How to Find the Ground State of a System of Identical Bosons?

    Suppose I have a system of N identical bosons interacting via pairwise potential V(\vec{x} - \vec{x}'). I want to show that the expectation of the Hamiltonian in the non-interacting ground state is \frac{N(N-1)}{2\mathcal{V}}\widetilde{V}(0) where \widetilde{V}(q) = \int d^3 \vec{x}...
  48. M

    Second Quantization and Field Operators

    When defining a field operator, textbooks usually say that one can define an operator which destroys (or creates) a particle at position r. What does this really mean? Are they actually referring to destroying (or creating) a state who has specific quantum numbers associated with the geometry...
  49. T

    How Do Energy Levels Interact When They Are Quantized?

    Pretty basic question: If energy levels (say, of an electron) are quantized, how is an interaction resolved wherein incoming energy (say, a photon) is not of an appropriate amount of energy to result in an appropriate response (say, moving from 1s to 2s in a simple hydrogen atom)? Suppose the...
  50. M

    Space quantization of electron orbits ?

    The values of theta that represent the angle b/w orbital quantum no. (l) & magnetic field direction can never by pi or 0 deg as then the magnetic quantum no . will have non integral values & and also the direction of orbital quantum no . & magnetic field will be parallel which means the electron...
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