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. T

    Bohr Quantization Rule for Angular Momentum

    Use the Bohr quantization rules to calculate the energy levels for a harmonic oscillator, for which the energy is p²/2m + mw²r²/2; that is, the force is mw²r, where w is the classical angular freq of the oscillator. Restrict yourself to circular orbits. So far I have that mvr=nh\, w=v/r, and...
  2. Q

    Quantization and fluid mechanics?

    Quantization and fluid mechanics?? Cant quantum field theory be applied to releativistic imcompressible fluids? cant the velocity vector field be quantized? will the pressure of the fluid play the role of the 4th component of the four vector? what would be the corresponding quanta? (I know...
  3. N

    Understanding Mass Quantization in Elementary Particles

    Mass Quantization! Homework Statement Elementary particles seem to have a discrete set of rest masses.Can this be regarded as quantization of mass? Homework Equations The Attempt at a Solution No,the rest masses are not found to be integral multiple of some fundamental mass unit...
  4. C

    Quantum Effects on Energy Levels: The Relationship between Heat and Work

    i understand that adding heat to an atom will cause the electrons to populate higher energy levels... but apparently doing work will cause the energy levels themselves to change (increase i guess?) Is this true and if so why?! Thanks!
  5. W

    Quantization of linear momentum

    This question deals with the Wilson-Sommerfelt quantization rule: (integral) Pdq = nh The first part of my question asks you to derive Bohr's quantization condition from this, with the hint that angular moment does not depend on the angle. That part I got. The second part asks, in...
  6. Q

    Photon Question-Energy Quantization Question-

    Photon Question-Energy Quantization Question---please help! This is a somewhat simple question I'm just unsure what relations to use. I found an equation relating number of protons to power and frequency but I'm not sure how to apply it to this case. EQUATION? Power = energy per unit time...
  7. R

    Field Quantization: Is "Forces Exchanged by Particles" a Deep Concept?

    When quantizing a static force field, say a Coulomb field, we get off mass shell, virtual particles and we say they transmit the force between two charges. They say the exchange of particles produces a force. It's a very profound and important concept in physics. But then, as I read many...
  8. E

    Second Quantization: Momentum, Kinetic & Potential Energies + 2 Particles

    Write momentum, kinetic and potential energy, and two particle interaction in second quantization. That is the question that I need to answer for my exam, but I don't have any idea what second quantization is, except that you can solve harmonic oscilator by using ladder operators. I can't find...
  9. S

    Is Acceleration Quantization Valid in Quantum Mechanics?

    acceleration quantization ?? If x \Psi (x,t)=x \Psi(x,t) and p \Psi (x,t)= -i\hbar \partial _{x} \Psi (x,t) then should it be a \Psi (x,t) = \dot p \Psi (x,t)= \hbar ^{2} \partial _{xt} \Psi (x,t) using usual QM So, the direct quantization of motion equation (constraint) should...
  10. K

    Can we apply 'Quantization' only from motion equation ?

    Can we apply 'Quantization' only from motion equation ?? Supposing you have the equation of motion (in terms of momenta and position) F(\dot p_{a} , q_{a})=0 then can you obtain the 'Quantum analogue' without the intervention of the Lagrangian ? and another question could we regard...
  11. jal

    Spin foam model from canonical quantization

    The “math kids” are hard at work. http://arxiv.org/PS_cache/arxiv/pdf/0705/0705.3892v1.pdf Spin foam model from canonical quantization Sergei Alexandrov 26 may 2007 ----------- A quick search of dual 4-simplex found this supplementary information...
  12. D

    Quantization of EMR in charge acceleration

    If I accelerate a charge, EM radiation is emitted. For a simple dipole model, the radiation propagates outward along a torus shape (see Griffiths, Intro to ED, 3ed., fig 11.4) - the acceleration field, with power according to Larmor formula. Since EMR is quantized, in what way is the described...
  13. X

    Understanding Quantization Effects

    I am obtaining data with a sample rate of 6250 samples/second on a digital oscilloscope. Ideally, I am obtaining a sinusoid output through a system from a sinusoid input. My expected results through the system are lower in amplitude than I am actually recording. I have some reasons for why...
  14. A

    What is the theoretical proof of the quantization of the energy of the EM field?

    Hi, The energy of the quantum mechanical harmonic oscillator is proved to be quantized after solving the Schrodingers equation which leads to Hermite equation and discovering that normalizable solutions of the wavefunction exist only for a discrete spectrum of energy. When the...
  15. S

    BRST quantization of string question

    Hi, I am confused about the following, I was hoping someone could help: The context: Polchinski Ch. 4.2, specifically equations 4.3.1a-c I am verifying the BRST invariance of the bosonic string action (after one has integrated out B, and the weyl ghost),, I notice that one must use the...
  16. W

    Reflection and Quantization of Energy Levels

    From what I have been reading, the reflection of light from an object, like th eyellow color of sulfur is the same phenomenon as Rayleigh scattering. It seems that the electrons receive the incoming photon and are raised to a higher "virtual energy state." When they return to the ground state...
  17. R

    Is Quantum Movement Similar to Teleportation in Subatomic Particles?

    I have been reading some on QM and its quantization of energy and angular momentum (is this the same as spin?). But something I do not understand is the actual process of quantizational movement (which is tied to the quantization of energy). I can't understand how a subatomic particle, the...
  18. M

    Relativistic Energy Quantization for Particle in Box

    How would you go about finding the energy for "the particle in a box" when the particle is relativistic? Since the energy is no longer p^2/2m, then the general quantization won't apply. I know that the two principles that still apply even when a particle is relativistic are: \lambda =...
  19. L

    Is Angular Momentum Quantized Due to Non-Commutable Rotations?

    You can define angular momentum for a free particle, with respect to another particle? i.e. L = v x r? This kind of angular momentum, would it be quantized? thanks Laura
  20. L

    Is Direct Brute Force Quantization Possible for Equations of Motion?

    "Brute force" quantization.. Let's suppose we have the "Equation of motions" for a particle: F(y'',y',y,x)=0 my question is if exsit a "direct" method to apply quantization rules..for example simply stating that: F(y'',y',y,x)| \psi (x) >=0 or something similar. - I'm not...
  21. L

    Quantization on momentum space

    I have this doubt..quantization in momentum space using G(p) as the Fourier transform of the wave function was not common (at least when i studied Q. Physics) my doubt is, if we have that: x |G(p)>=i \hbar \frac{ \partial G(p)}{\partial p} But..what would happen if we apply: \dot...
  22. S

    What is the role of the einbein in BRST quantization?

    In J.W. van Holten's essay Aspects of BRST Quantization ,hep-th/0201124, he begins (Section 1.1) with the free relativistic particle. In order to derive the dynamics from the action principle he introduces an auxiliary variable: a bit later he notes I thought I was really familiar with...
  23. E

    Quantizing Velocity: Exploring the Celerity Operator in Lagrangian Mechanics

    Let be the Lagrangian of a particle: L(q,\dot q,t) my question is if we can get its quantizied version in the form: p\dot q-L(q,\dot q,t)| \Psi>=E_{n}|\Psi > of course we know how to quantizy the Momentum operator the question is..¿how do we quantizy the "celerity" \dot q...
  24. Z

    Field Quantization: Confined in Cube or Whole Space?

    I see in many textbooks that all authors start field quantization with EM field confined in a cube of finite size, certainly some B.C. is imposed, usually periodic B.C., finally the cube goes to whole space. I have some questions on this procedure: 1, Is periodic(or other) B.C. reasonable...
  25. DaTario

    Why the name Second Quantization ?

    Why the name "Second Quantization"? Hi all, The title said it all. My question is: How is one to interpret the name second quantization ? Which specifically is quantized twice ? Best Wishes DaTario
  26. Y

    Field Quantization: SHOs vs Bounded States

    i have read through a mathematical description of the quantization of the electric field through the simple harmonic oscillator raising/lowering operators. what is the physical interpretation and justification for this? what if one assumes that photons do not behave like simple harmonic...
  27. E

    Quantization over quantization

    let,s suppose Bohmian mechanics was true then we would have trajectories in the form: m\frac{d^{2}x}{dt^2}=-\nabla(V+U_{b}) (1) U_{b}=-\frac{\hbar^2}{2m}\nabla^{2}\psi being psi the solution to schroedinguer equation...but the trajectories in (1) comes from the Hamiltonian.. H=H_0+U_b...
  28. kakarukeys

    A question about Dirac's quantization

    In his book Lectures on Quantum Mechanics, Dirac gives his way of quantizing system with contraints. I do not understand the use of weak inequality in some equations. C \approx 0 What is that for?
  29. B

    What Does Quantizing a Field Really Mean in Quantum Field Theory?

    Hi, I am currently trying to read Chapter 2 Peskin & Schroeder (PS) QFT. There are basics questions that bugging me so much. 1. The road from classical particle to QF. So particle in classical mech is discrete right, and we take a continuous aproach to make it into classical field...
  30. S

    Quantization of Energy: Does Mass Follow?

    Since energy only exists in quanta, does this mean mass is also quantized according to einstein's famous equation?
  31. C

    Understanding Quantization of Energy: Can We Produce EM Waves of Any Energy?

    Quantization of energy... We say that electrons have set energy levels, and certain energies they cannot possesses whilst in a certain atom. Is it still possible to produce photons / EM waves of any energy we desire? I mean, by looking at the equation E = hf it would appear we can - if we put...
  32. E

    Dynamical Quantization: A Non-Lagrangian Approach - Explained and Explored

    I read about it in the web,it,s suosed to be a quantizaton not nvolving lagrangians or Hamiltonians..could someone give me a link about dynamical quantization?..thanks.
  33. N

    Predicting Energy Quantization in CM Systems

    Are there any systems in CM where quantization of energy is predicted?
  34. I

    Question on Canonical Quantization

    This semester I took a course in Quantum Field Theory. It is difficult (the professor assumes you know everything) and I have so many questions... Starting with a lagrangian density, I was told that canonical quantisation is a procedure where we impose the usual commutation relation between...
  35. marlon

    Why is Electric Charge Quantized?

    This is why electric charge is quantized. See the zip-file if this word-doc regards marlon
  36. E

    Quantization of Mass: Exploring the Fundamental Building Blocks of Matter

    i have drawn an analogy with the quantization of radiation(EM).the motivation behind this thought was "what is the most elemetary particle?"u may say quarks but i can divide it further if i have high energy particles,so then where is ending for this?i thought it's better not end up in point...
  37. Antonio Lao

    What is the Connection Between the Graviton and the Higgs Boson?

    The quantum theory of field is sometimes known as second quantization. There are two distinct types of field in physics: 1. Scalar field. 2. Vector field. For each field, a force is supposed to be associated with it. But for the scalar field, this force is zero. This zero-force...
  38. arivero

    Isham's New Quantization & Topos Theory

    Readers of gr-qc could have lost the preprint from Isham at quant-ph this January, Quantising on a category http://arXiv.org/abs/quant-ph/0401175 I guess it is related to his series A New Approach to Quantising Space-Time ( gr-qc/0303060 gr-qc/0304077 gr-qc/0306064 ) which is so abstruse...
  39. E

    Quantization without Lagrangians.

    In fact let us suppose we only have the classical equations of movement x´=f(x1,x2,x3...xn) but we do not have or not know a lagrangian ..how could we quantizy them?..in fact how is a quantization made if we do not have a lagrangian (or hamiltonian)?..
  40. E

    Quantization of Minkowskian metric?

    I would like to know how you could apply quantum gravity for Minkowskian or F.R.W metric...that is how you can get the quantum version of the metric Gab for these two problems is there a solution?..What is the method used?..thanks.
  41. E

    Quantization Doubts: Techniques, P & Functional Derivative

    I have some soubts on quantizying theories..how many techniques are there?..is always as simple as to take p=-ihd/dx ?..or the functional derivative?..thanks.
  42. E

    Third Quantization: Definition, Usage & Maths

    What is called in physics the third quantization?..what is used for... and what is its math background?..
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