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. A

    Dose E=hn means quantization of energy?

    I have an example class yesterday, but one question troubled me. In part (b), why does E=nhf? For me, it seems E=nh is enough, why does the equation involve frequency f after quantization?
  2. P

    Ultraviolet catastrophe and quantization

    Homework Statement I'm taking physical chemistry 2 right now and we are discussing the basics of quantum mechanics, and I'm trying to understand black body radiation and the ultraviolet catastrophe. What I don't understand is how quantization and Plancks distribution fix the ultraviolet...
  3. P

    Plank's constant, phase integral and quantization of action

    I apologize in advance if this is too trivial, but... Time and again, I hear something along the lines of "Plank's constant is a unit of action", or "Plank's constant is a unit of action in the old quantum theory". In addition, many texts imply some sort of connection between quantization of...
  4. F

    What is 3rd quantization and what can be learned from it?

    I've heard that the quantum mechanics of particles in a potential is called 1st quantization which produces wavefunctions. And I've heard that quantum field theory is called 2nd quantization which in turn quantizes the wavefunctions. Can this process be iterated to give 3rd quantization, and...
  5. A

    Schrodinger Quantization VS Bohr Quantization

    Homework Statement What are the similarities and differences between the quantization of angular momentum in the Schrodinger theory and in the Bohr model? Homework Equations ? The Attempt at a Solution Similarities: -In both theories, the principal quantum #, n, determines the...
  6. M

    Second quantization question: one particle or n particle?

    For the simple harmonic oscillator case, the energy is E=(n+1/2)hw, and N|n>=n|n>. It seems second quantization explain it as there are n bosons with each particle has energy homework plus vacuum 1/2hw. But we know before second quantization, there is only one particle with energy nhw plus...
  7. E

    Second Quantization: Motivation & Field Operators

    Hi,all What is the motivation of using Second Quantization ? What kind of situation does people want to use field operators ? Euphemia
  8. D

    Quantization of vector field in the Coulomb gauge

    I have a technical question and at the time being I can't ask it to a professor. So, I'm here: If I try to quantize the vector field in the Coulomb gauge (radiation gauge) A_0(x)=0,\quad \vec\nabla\cdot\vec A=0. by imposing the equal-time commutation relation...
  9. xaratustra

    Landau quantization of cyclotron orbit

    I don't know what the speed of light c is doing in the Hamiltonian for the Landau quantization. The term doesn't have dimensions of momentum anymore. :confused: \hat{H}=\dfrac{\hat{p}^2_x}{2m}+\dfrac{1}{2m}\left(\hat{p}_y-\dfrac{q|\vec{B}|}{c}\hat{x}\right)^2 Any ideas? thanks.
  10. fluidistic

    Question related to quantization of the magnetic field

    I wonder what happens if you have trapped hydrogen atoms and you apply a magnetic field. We could observe the Zeeman effect; some electrons would gain energy and some other would lose energy due to the magnetic field. Say an electron gained some energy. Now you remove the magnetic field, the...
  11. C

    Solving the Integral present in Dirac's quantization of charge problem

    Homework Statement This problem involves an electric monopole placed at the origin and a magnetic monopole placed a distance D away, say arbitrarily, along the z-axis. I need to compute the angular momentum of the EM fieds: \vec{J_{field}} = \frac{1}{4\pi c}\int{d\tau \vec{r} \times...
  12. M

    Quantization of electromagnetic field

    Instead of quantizing the vector potential A^μ why we do not directly quantize the B and E fields in electrodynamics.
  13. F

    Path Integral in first and second quantization

    Is it true that in first quantization the PI includes the possible trajectories a particle can take, but it does not include how particles can change into other kinds of particles (electrons to photons, etc). And QFT (second quantization) calculates how particles can branch off into other...
  14. D

    What is Planck's Quantization of Energy?

    Homework Statement I don't understand what E = nhv means. What does it apply to and what does the n (energy level) mean in the equation. It says in the textbook, "According to Planck, the atoms of the solid osscillate with a definite frequency depending on the solid. But in order to...
  15. F

    Lowest Landau Level Resistance Quantization

    For a 2D system of N electrons in the presence of a perpen B field and parallel E field the resistance comes out quantized proportional to h/e. And I know this result can be obtained by finding the probablity current for the lowest Landua level wavefunction. But isn't the resistance...
  16. nomadreid

    Does the Quantization of Space-Time Imply a Finite Number of Spatial Locations?

    If space-time itself is quantified, and the spatial universe has, at anyone time, a finite volume, would this not imply that at anyone moment there are a finite number of spatial locations? (If so, then integrating over an infinite number of points would only give an approximation.)
  17. bcrowell

    Quantization of mass for black holes?

    "Black Hole Masses are Quantized," Gia Dvali, Cesar Gomez, Slava Mukhanov, http://arxiv.org/abs/1106.5894 There is a nontechnical summary on the arxiv blog: http://www.technologyreview.com/blog/arxiv/ , along with some inflammatory and uninformed speculation about safety at the LHC, including...
  18. T

    Second quantization derivation of spin-orbit coupling.

    Can anyone recommend books/reviews that derives the spin-orbit coupling in second quantization. I am working on a tightbinding model and I should be able to convert the spin-orbit hamiltonian from k-space to atomic representation using Warnier states, but I can't figure out some of the aspects...
  19. R

    Why Is It Called Space Quantization in Quantum Mechanics?

    I'm not quite sure which forum I should post this in; it's related to my school work but I don't have any homework questions about it. Rather, I am just confused about what it really is and what it means. Hopefully it goes here. I get that the projection of the angular momentum along some...
  20. F

    1st to 2nd quantization, potential approximates interactions?

    I'm wondering if the potential term in the Lagrangian for a single particle is just an approximate way to summarize all the interactions of virtual particles created by the potential at every point. For example, the EM field is mediated by photons at every point in space. In reality an electron...
  21. N

    Grassman number in functional quantization?

    Please teach me this: When calculating something with Grassman numbers without changing order of the numbers,then there are nothing different from ordinary numbers.So I think it would be contrary if we define the complex conjugation of a product of two Grassman numbers to reverse the order of...
  22. J

    Charge Quantization: Exploring e, Q, g & Weak Charges

    I'd like to focus in on some info from a previous thread that seemed too good to pass up https://www.physicsforums.com/showthread.php?p=3156965 Yes I was making that confusion, and I'd like to understand this a bit better. I have three questions to follow up if you don't mind. Is there a...
  23. Q

    Understanding Second Quantization and Its Application in Quantum Mechanics

    I begin with \int (\bar{\psi}(x) (\mathcal{H} \psi(x)) d^3x This is just \int (\bar{\psi}(x) ({\frac{p^2}{2M} + \frac{1}{2}M \omega^2 (x)} \psi(x)) d^3x If one identified that \bar{\psi}(x) and \psi(x) are creation and annihilation operators, I assume that I can simply restate my...
  24. C

    Scattering Amplitude in Canonical Quantization

    Hi there, I have little question: reading zee 2nd edition, I.8 (pag 64) i came up with this: start with <k_1 k_2| e^{-iHT}| k_3 k_4> and H=H_0 +u u=\lambda \int \phi^4 where H_0 is the usual hamiltonian for the free scalar field. Then, zee says that "expanding in \lambda, we obtain...
  25. U

    In the second quantization spin operator, what are Pauli spin vector indices?

    If you look up the second quantization spin operator, you'll notice that there are two indices on the pauli vector for two possible spins. The operator sums over these two indices. Since the pauli vector is an unchanging quantity what do these indices physically correspond to?
  26. N

    Second Quantization: Explaining c^\dagger_ic_j = \delta_{i,j}c_jc^\dagger_i

    Hi Say I have the following two fermionic creation/annihilation operators c^\dagger_ic_j 1) Yesterday, my lecturer said that the following is valid c^\dagger_ic_j = \delta_{i,j}c_jc^\dagger_i Can you guys explain to me, where this formula comes from? I originally thought that it was one...
  27. D

    Commutators in second quantization

    Hi. I've been trying to calculate a couple of commutators, namely [\Psi(r),H] and [\Psi^{\dagger}(r),H] where H is a free particle hamiltonian in second quantization. I have attached my attempts and I would greatly appreciate if anyone could tell me if I am right or if there is a better way to...
  28. H

    Second Quantization: Exploring the Strange Results

    Didnt seem to be many threads about this subject although I don't find it trivial at all.. Lets start with a question: If we now have <N_i - 1|â_i|N_i> = N_i^0.5 but let â operate on our ket it should give: <N_i - 1||N_i - 1> = N_i^0.5 its adjoint however is the creation operator (right?)...
  29. G

    Quantization of Klein-Gordon Field

    I was reading the book written by Peskin about QFT when I found that the following equation: (\frac{\partial}{\partial t^2}}+p^2+m^2)\phi(\vector{p},t)=0 has as solutions the solutions of an Harmonic Oscillator. From what I know about harmonic oscillators, the equation describing them should...
  30. N

    Second Quantization: Explaining Creation/Annihilation Operator Transformation

    Hi I have a question regarding second quantization. In the following link...
  31. S

    Landau Quantization: Classical Particle Motion in a Uniform Magnetic Field

    1. The problem statement Problem: "Consider a classical particle with charge q and mass m in 2 dimensions (xy-plane) moving in the presence of a uniform magnetic field B=B_z.'' There are a number of parts to this problem, but it's the first three that have me confused. "(a) Describe the...
  32. D

    Second quantization particle current

    Hi. I'm reading an article which writes the following "... and the well-known expression for the charge current is" j=-\frac{ie}{m}\int dr\psi^\dagger (r)[\nabla-ieA(r)]\psi(r) Why does it have an integral sign? And when you define it this way, you integrate out the r-dependence...
  33. S

    Quantization to solve black body radiation

    Homework Statement how does Planck's idea of quantization of the energy found in electromagnetic waves solve the problem of black body radiation? Homework Equations N/A The Attempt at a Solution this is what i have said correct me if I am wrong... so plank said that photon has...
  34. D

    Express arbitrary state in second quantization

    How do I express an arbitrary 2-particle state in second quantization? I could write this |\psi\rangle=\sum_{mn}c_{mn} a_m^\dagger a_n^\dagger |0\rangle where c_{mn} is a constant, a_n^\dagger is the creation operator and |0\rangle is the vacuum state. The only problem is that I want to...
  35. tom.stoer

    Quantization = construction of quantum theories based on the classical limit?

    I have a question regarding quantization. In most cases one never starts with a quantum theory, but always writes down a classical expression, goes through quantization, implementation of constraints (Dirac, BRST, ...), construction of Hilbert space, inner product, measure of an path integral...
  36. N

    Does the New Quantization Method Redefine Time Symmetry in Quantum Mechanics?

    A new quantization method for relativistic fields has been recently proposed. Compact time naturally reproduces canonical quantum mechanics as well as the path integral formulation, and in a deterministic way (no hidden-variables)! It seems to be a new way of thinking to the concept of time...
  37. Z

    Semiclassical Bohr quantization with a magnetic potential

    Homework Statement given the Hamiltonian in one dimension H= \frac{(p-eA)^{2}}{2m}+ V(x) use the Bohr-Sommerfeld quantization in one dimension to obtain n=n(E) Homework Equations Hamiltonian , quantization The Attempt at a Solution from the usual quantization algorithm in one dimension i...
  38. K

    What is the Maximum Quantization Error Voltage in a PCM System?

    Homework Statement Q1 A linear PCM system has an input signal 2cos6000PIt volt. Determine, (a) the minimum sampling rate required, (b) the number of bits per PCM codeword required for a signal to quantization noise ratio of at least 40 dB, (c) the maximum quantization error voltage, (d)...
  39. L

    Canonical Quantization of KG field

    Hi, for my exam i"m re-reading Peskin&Schroeder and stumbled across equations 2.21-2.25 where the canonical quantization of the KG field is done. P&S start with doing a Fourier trf on \phi(x,t)=\int\frac{d^3p}{(2\pi)^3}e^{ip\cdot x}\phi(p,t) applying the KG operator in that results in...
  40. N

    Second quantization operators

    Hi guys The fermionic creating and annihiliations operators: Do they satisfy c_{i,\sigma }^\dag c_{i,\sigma }^{} = - c_{i,\sigma }^{} c_{i,\sigma }^\dag for some quantum number i and spin σ, i.e. do they commute?
  41. E

    Canonical vs. path integral quantization

    Hey folks, i have a question concerning canonical and path integral quantization. From what I have understood so far, these two techniques are different and independent but equivalent. My problem is that I don't really see where the quantum character enters in the path intregral formulation...
  42. H

    Exploring the Hydrogen Atom: 1s Electron Distance & Quantization

    1. The most probable point a 1s electron will be found in the hydrogen atom is r = 0. 2. The most probable distance that a 1s electron will be found in the hydrogen atom is r = 0. 3. For a hydrogen atom with l (lower case L) = 0, Ψ is independent of the angles Θ and Φ. 4. For a hydrogen atom...
  43. K

    Question about quantization of Lz

    I'm being asked on a homework to show that the m orbital angular momentum quantum number can only take integer values. Using ladder operators I know how to prove that m is restricted to half-integers, but I'm having trouble with a further restriction. I'm quite certain the problem does not want...
  44. N

    Interpreting operators in second quantization

    Hi guys When working with operators in second quantization, I always imagine c^\dagger_ic_j as denoting the "good old" matrix element \left\langle {i} \mathrel{\left | {\vphantom {i j}} \right. \kern-\nulldelimiterspace} {j} \right\rangle . But how should I interpret an...
  45. MTd2

    EPRL quantization found to be completely inconsistent.

    http://arxiv.org/abs/1004.2260 The new vertices and canonical quantization Sergei Alexandrov (Submitted on 13 Apr 2010) We present two results on the recently proposed new spin foam models. First, we show how a (slightly modified) restriction on representations in the EPRL model leads to...
  46. V

    Clarifying Boundary Conditions and Scalar Field Quantization in QFT

    This commmunity has so many nice people, so helpful, I am learning QFT from Srednicki I would be glad if some one can clarify, all the books talk about boundary conditions which are finite at spatial infinity and give the general solution for canonical quantization of scalar field, 1) how...
  47. JK423

    Is light really a particle or a wave?

    I'd like to ask one 'newbie' question on the quantization of the E/M field. I know that when we quantize the E/M field we get infinite in number harmonic oscillators. I just want to know, what's the 'physical meaning' of these harmonic oscillators? How do we interpret this result...
  48. N

    Free particles in second quantization

    Hi guys Today my lecturer talked about second quantization, and at the end he talked about free fermions in second quantization. He said that free electrons in second quantization satisfy that their Hamiltonian is only written as a linear combination in terms of c^\dagger c (the creation and...
  49. M

    Landau quantization and magnetic translation

    I am trying to learn the integer quantum hall effect and have a pretty straightforward question. I understand that the normal translation group does not commute with the Landau Hamiltonian. Does this mean that if you have a state in the lowest Landau level (LLL) and apply the translation...
  50. N

    Second Quantization: Creation & Annihilation Operators

    Hi all I am reading about second quantization. The kinetic energy operator T we write as \hat T = \sum\limits_{i,j} {\left\langle i \right|T\left| j \right\rangle } \,c_i^\dag c_j^{}. Now, the creation and annihilation operators really seem to be analogous (in some sense) to the...
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