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. Einj

    Second quantization operators

    I have a doubt on the second quantization formalism. Suppose that we have two spin-1/2 fermions which can have just two possible quantum number, 1 and 2. Consider the wave function: $$ \psi(r_1,r_2)=\frac{1}{\sqrt{2}}\left(\psi_1(r_1)\psi_2(r_2)-\psi_1(r_2)\psi_2(r_1)\right). $$ The second...
  2. W

    General Quantization of Motion in Circular Orbits

    For this question, I have to obtain a general quantization of motion in circular orbits by combining the equations (Where U(r) is potential energy): (mv2)/r= |(dU(r))/dr| With the angular momentum quantization of: mvr= nℏ Then use this to calculate the spectrum for circular motion in a...
  3. N

    What are the difficulties of gravitational quantization scheme?

    I will study gravitation quantization(string theory or canonical quantum gravity),so I want to know what are the difficulties of gravitational quantization scheme.I know that quantization means that calculating commutator of quantum field operators via Poisson brackets.Are the difficulties being...
  4. K

    Quantization Postulates for a Particle

    Show that the operators x^2 p_x^2+p_x^2 x^2 and 〖 (xp_x+p_x x)〗^2/2 differ only by terms of order ℏ^2. The attempt at a solution is attached (Postulates.pdf)
  5. M

    Speed of light - quantization

    I beg my pardon in advance for the stupidity of my question. Is there any "Behind the standard model" paper, document, crazzy theory, essay... exploring a universe where the speed of the light would have several upper limit: c, 2c, 3c, ... N. c? (with c = 3. 108 meter/second) That is.
  6. V

    Preservation of Poisson Bracket Structure upon quantization?

    When (canonically) quantizing a classical system we promote the Poisson brackets to (anti-)commutators. Now I was wondering how much of Poisson bracket structure is preserved. For example for a classical (continuous) system we have $$ \lbrace \phi(z), f(\Pi(y)) \rbrace = \frac{\delta...
  7. A

    Second Quantization: Single Particle Basis States

    This is just a simple question. I am reading about the second quantization but every text I read it starts with something like: suppose we have a set of single particle basis states {la1>,la2>,...,lan>}, which are used to label the wavefunction etc. I just need to make sure I understand what...
  8. A

    Second quantization of the Schrodinger fields

    Hi, I'm reading www.phys.ethz.ch/~babis/Teaching/QFTI/qft1.pdf and trying to understand the canonical quantization of the Schrodinger field. In particular, the Lagrangian: \begin{equation} \mathcal{L} = \frac{i}{2}\psi^* \partial_0 \psi - \frac{i}{2}\psi \partial_0 \psi^* +...
  9. wolram

    Quantization of Gravity: Testing with CMBR Polarization | Krauss, Wilczek

    A short but interesting way of using the CMBR to test the quatization of gravity, what do you think ? Lawrence M. Krauss (1,2), Frank Wilczek (3) ((1) Arizona State University, (2) Australian National Univeresity, (3) MIT) (Submitted on 20 Sep 2013) While many aspects of general...
  10. B

    What are the Different Formulations of Quantum Mechanics?

    In classical mechanics you construct an action (involving a Lagrangian in arbitrary generalized coordinates, a Hamiltonian in canonical coordinates [to make your EOM more "convenient & symmetric"]), then extremizing it gives the equations of motion. Alternatively one can find a first order PDE...
  11. S

    Electromagnetic field quantization

    1. Hey, So I have to show this proof: \int d^{4}x(-\frac{1}{4}F_{\mu\nu}F^{\mu\nu})=\frac{1}{2}\int d^{4}xA^{\mu}(\square n_{\mu\nu}-\partial_{\mu}\partial_{\nu})A^{\nu} 2. Where F_{\mu\nu}=\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu} 3. ok, so I spent forever trying to type...
  12. tom.stoer

    Old Quantum Theory & Quantization of Action

    "Old quantum theory" was derived using "quantization of action" in phase space ##\oint p\,dp = nh## Does "quantization of action" still make sense using canonical quantization?
  13. M

    Understanding the Role of the Quantization Axis in Angular Momentum Measurements

    What is quantisation axis? In many books authors just say that we choose that z is quantization axis.
  14. M

    Quantization of Energy in Quantum Mechanics - Real Examples?

    Why this quantization of energy term occur in quantum mech? Why this "quantization of energy" term occur in quantum mech? Is there any real physical example of quantization of energy? or its just a thought? As i know that if a particle is bound in between two potential walls then the energy of...
  15. N

    Quantization of hamiltonian with complex form

    In most of textbooks, the canonical quantization procedure is used to quantize the hamiltonian with a simple form, the quadratic form. I just wonder how should we deal with more complex form hamiltonian, such like the ones including interaction terms?
  16. S

    Does quantization mean there are only so many colors?

    Given that a photon of known wavelength is emitted when an electron goes to a lower energy state, if there are only so many different types of atoms, and only so many electron orbits around those nuclei, the number of wavelengths possible is finite: If true, then the EM spectrum is quantised...
  17. T

    Proof of second quantization operators

    Please, can somebody show me why a Hamiltonian like \sum_nh(x_n) can be written as \sum_{i,j}t_{i,j}a^+_ia_j, with t_{i,j}=\int f^*_i(x)h(x)f_j(x)dx? Thank you.
  18. E

    De-Broglie's explanation on Bohr's Angluar Momentum quantization?

    In order to understand about De-Broglie's explanation on Bohr's second postulate,concept of standing waves should be understood. But condition of λ for a given value of length(string) L is given by L=nλ/s where n =1,2,3 etc. But for a string whose ends are connected together and its shape is...
  19. H

    General quantization of circular motion/spectrum in potential

    Homework Statement The general quantization of motion in circular orbits is obtained by combining the equation of motion ## \frac{mv^2}{r} = |\frac{dU(r)}{dr}| ## with the angular momentum quantization condition ## mvr=n\hbar ## Use this procedure to calculate the spectrum for circular...
  20. H

    Is my understanding of EM field quantization correct?

    Essentially how I understand it is, (this is for the quantization of an EM field in vaccum) -Fields become operators, a specific E operator will contain the number and multiple of rising and lowering operators needed to raise a vacuum state into the desired quantum state -The electromagnetic...
  21. Y

    State space of QFT, CCR and quantization, and the spectrum of a field?

    State space of QFT,CCR and quantization,spectrum of a field operator? In the canonical quantization of fields, CCR is postulated as (for scalar boson field ): [ϕ(x),π(y)]=iδ(x−y) ------ (1) in analogy with the ordinary QM commutation relation...
  22. V

    Inverse Weyl quantization of the projection operator.

    I am trying to solve the following problem on an old Quantum Mechanics exam as an exercise. Homework Statement Homework Equations I know that the trace of an operator is the integral of its kernel. \begin{equation} Tr[K(x,y)] = \int K(x,x) dx \end{equation} The Attempt at a...
  23. michael879

    Quantizing Bosons: Is Classical Wave Theory Compatible with Experiments?

    This is just an idea I had, but I can't seem to find any obvious flaws with it. It's pretty clear that the only description we have of fermions is as quantum objects. There is just no classical analog! Bosons however, have a very natural classical analog. If you just treat the quantum fields...
  24. E

    Quantization of Energy: Planck's Constant & Standing Waves

    I have a basic problem about Planck's quantization of energy, ε=hv. It's said that we can only get the integer product of hv, that's the quantilization. But when we plug in v, we can plug any continuous value? Does that mean a particular standing wave in a capacity is specifield a particular v...
  25. A

    Why spacetime quantization does not prevent blackhole formation?

    Hi, This is my first post and first of all I would like to thank all the contributors to this forum for the amazing amount of information provided here. I’m not a physicist, but I like physics (although I have only a qualitative understanding of it) and I like to smash my brain on difficult and...
  26. J

    Second Quantization for Fermions: Creation Operator

    So, I'm studying Second Quantization for fermions and came across this equation. I was just wondering why there is a summation needed? And why do we do it with (i≠p).? Please can someone explain this to me? Reply and help is much appreciated.
  27. N

    QM: Understanding Quantization Axis for 2-Level Atoms

    Hi I have a question on how to work with quantization axis. The setup I am looking at is a single two-level atom placed at the origin (0, 0, 0), which is not perturbed by any magnetic field. I now send in a laser resonant with the transition of the atom. With a right-handed coordinate...
  28. J

    Spacetime Quantization and the Relationship between Energy and Frequency

    Consider a mode of vacuum zero-point energy at a point in space. Its energy E is related to its frequency f by E = \frac{1}{2}h f. In terms of the mode oscillation period \Delta t the energy is given by E = \frac{1}{2}\frac{h}{\Delta t}. Now let's us imagine that \Delta t becomes smaller and...
  29. J

    Second Quantization for Fermions

    Please let me know if I get this right. Second Quantization for Fermions used the definition of its annihilation and creation operators instead of wavefunctions. We use second quantization to express this many body problem in a hamiltonian. Am I right? Can someone please explain this to me in...
  30. S

    Shubnikov de haas oscillations, conductance quantization

    Hi all I'm just studying the QHE and Shubnikov de Haas oscillations. There are two points I find somehow confusing: 1. If you look at ρxx (resistance along the direction of applied field), you will find oscillations of this resistance as a function of the external magnetic field. Whenever...
  31. W

    No general quantization recipe?

    there is in general no exact recipe for quantization what does this mean? i think there is only one (correct) quantum mechanics
  32. S

    Quantization of angular momentum

    Imagine a semi-classical birdcage of radius R with N regularly spaced bars individually separated by a spacing a. Now imagine there is a linear light source centered along the cylinder's axis z. Use the dual wave/particle nature of light to show that angular momentum is quantized in the...
  33. L

    Quantization of energy in blackbody radiation

    I have been reading a lot of stuff on blackbody radiation and the ultraviolet catastrophe. Here is what I have so far. The ultraviolet catastrophe arises from the classical electrodynamics predicting an infinite amount of energy from a blackbody having any temperature. As far as I have...
  34. L

    Charge conjugation in second quantization

    We know that under charge conjugation the current operator reverses the sign: \hat{C} \hat{\bar{\Psi}} \gamma^{\mu} \hat{\Psi} \hat{C} = - \hat{\bar{\Psi}} \gamma^\mu \hat{\Psi} Here \hat{C} is the unitary charge conjugation operator. I was wondering should we consider gamma matrix...
  35. P

    Calculating Bits for Discrete-Time Signal Quantization

    Homework Statement Consider the following discrete-time signal where the samples are represented using N bits. x(k) = exp(-ckT)μ(k) μ(k) represents the unit step function and T is the Δ between each sample. -How many bits are needed to ensure that the quantization level is less than...
  36. S

    Secound Quantization: Definition, Meaning & Wavefunction ψ

    what is this concept, what are we getting or achieving?? what is the meaning of wavefunction ψ becoming an operator, If that is so, then what are states described by, what do eigen values of psi ψ suggest??
  37. Physics Monkey

    Is Singular Quantization Still Necessary for Loop Quantum Gravity?

    I recently bought "A First Course in Loop Quantum Gravity" by Pullin and Gambini. Partly, I was curious to see what, if anything, had changed in the pedagogy. I also got Bojowald's book a while back. In the final section of "A First Course ..." the authors discuss open problems and broad...
  38. N

    Atomic Physics: Quantization axis

    Homework Statement Hi I have a question - it is not homework, but something I have thought about for a long time. I really can't come up with a solution to the problem, and it is driving me crazy. Here is the problem: Say I have a linearly polarized monochromatic wave incident on an...
  39. N

    Can the Quantization Axis of an Atom Affect its Spectral Emission?

    Hi Please see the attached picture. It shows an atom, the filled black circle, which consists of a J=0 level (with m=0 sublevel) and J'=1 (with m' = +/- 1 sublevels). From the left is a nearly monochromatic laser impinging on the atom, which is linearly polarized along the same direction of...
  40. C

    K-Means vs. Minimum-Variance Quantization

    Hi, I have a situation where I have a set of n data points and want to specify k values that best approximate the values in the set. (it's an image-color reduction problem) MATLAB has a magic algorithm using something called minimum-variance quantization that will do this (although I...
  41. maverick280857

    Understanding AdS and quantization in AdS

    Hello everyone, For a project that may involve some work with Anti de Sitter space, I want to understand 1. what the AdS metric looks like 2. how to set up and solve boundary value problems in AdS, e.g. scalar field KG equation in AdS 3. how to quantize scalar fields in AdS For 1, I...
  42. J

    Energy quantization and energy levels

    Hello ! I had my fair share of quantum mechanics already :) But today I was wondering something, kind of odd I thought of this so late ... But do continuous energy levels really excist or is it just an approximation. I am asking this cause by my understanding energy is quantized, so...
  43. N

    Canonical Quantization problem; finding Schroedinget time-dependent equation

    Homework Statement A particle of mass m is confined in a Pösxhl-Teller potential as defined by: V(x) = -V0sech2(αx) Where V0 and α are constants representing the depth and width of the well. Use canonical quantisation to find the time-depndent Schrödunger equation for a particle in...
  44. O

    Relation between commutation and quantization

    relation between "commutation" and "quantization" Hi people; Over the several texts I have read, I got the impression that position-momentum commutation relations is the cause of "quantization" of the system. Or, they are somehow fundamentally related. The only relation I know of, is to...
  45. quasar987

    Simplest example where quantization is unknown

    As I understand (from reading p. 2-06 of Marle's 1975 text on geometric quantization available on the french wiki page on "quantification géométrique") , there are physical situations where we do not know how to write the Schrodinger equation. Namely, we do not know what operator to take as the...
  46. marcus

    How close to QG now with cellular quantization?

    There is an issue with the new paper by Bonzom and Smerlak on cellular quantization of geometry, which surfaces in an obscure footnote #5 on page 5 at the end. The paper http://arxiv.org/abs/1201.4996 appears to resolve most or all of the outstanding doubts concerning the Loop program. That...
  47. D

    First, second and third quantization formalisms

    Hi all, I was curious about mathematics and physical meaning behind first and second quantization formalisms of schrodinger's equation. what do these mean? Okey, third quantization formalism may be weird/new for many but its associated with wheeler dewitt equation.
  48. F

    Density matrix elements, momentum basis, second quantization

    Hello everyone, I'm having some trouble, that I was hoping someone here could assist me with. I do hope that I have started the topic in an appropriate subforum - please redirect me otherwise. Specifically, I'm having a hard time understanding the matrix elements of the density matrix...
  49. T

    Path Integral/Canonical Quantization of Gauge Theories

    I'm really getting frustrated right now, as I am unable to reproduce the two-point gauge-field correlation function (i.e. propagator) as derived from the path integral in an R_\xi gauge using operators from canonical quantization. I believe the polarization 4-vectors of the gauge field ought to...
  50. S

    Graviton Quantization: Energy Needs of Particle Accelerator

    Theoretically, how much energy in particle accelerator would be required to quantize a graviton from a gravity field?
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