Quantization Definition and 24 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. dextercioby

    A Wiesendanger's quantization of an SO(1,3) extension of GR

    Are you aware of the 3-article series of Wiesendanger's quantized extension of GR? This is open access: C Wiesendanger 2019 Class. Quantum Grav. 36 065015 and the two sequels linked to in the PDF. The question is if this work counts as a quantization of a reasonable extension or reformulation...
  2. Boltzman Oscillation

    What is the difference between PCM and quantization?

  3. Riotto

    A Canonical momentum ##\pi^\rho## of the electromagnetic field

    In David Tong's QFT notes (see http://www.damtp.cam.ac.uk/user/tong/qft/qft.pdf , page 131, Eq. 6.38) the expression for canonical momentum ##\pi^0## is given by ##\pi^0=-\partial_\rho A^\rho## while my calculation gives ##\pi^\rho=-\partial_0 A^\rho## so that ##\pi^0=-\partial_0 A^0##. Is it...
  4. maajdl

    A Canonical quantization of Electrodynamics: physical intuition ?

    Hello, I am freshly retired and enjoy going back to the fundamentals. I followed the wonderful courses by Alain Aspect on Coursera on Quantum Optics 1 and 2 . The quantization of Electrodynamics is really easy stuff. Just follow the correspondence between Poisson brakets and Commutators ... and...
  5. Alan Ezra

    I Particle in a box and quantization of energy

    Greetings, In the scenario of a particle in an infinite potential well, there are discrete energy levels, i.e.##E=\hbar ^2 n^2 \pi ^2/ (2 m L^2)## where L is the width of the potential well, and n takes on positive integers. But what will happen if I put a particle of energy ##E_i## that is not...
  6. Auto-Didact

    A Quantization isn't fundamental

    This thread is a direct shoot-off of this post from the thread Atiyah's arithmetic physics. Manasson V. 2008, Are Particles Self-Organized Systems? The author convincingly demonstrates that practically everything known about particle physics, including the SM itself, can be derived from first...
  7. It's me

    Show that the radiation field is transverse

    Homework Statement Show that the radiation field is transverse, ##\vec{\nabla}\cdot\vec{A}=0## and obeys the wave equation ##\nabla^2\vec{A}-\frac{1}{c^2}\partial_t^2\vec{A}=0##. You should start from the expansion of the quantum Electromagnetic field. Homework Equations ##H=\frac{1}{2}\int...
  8. N

    Quantizing the complex Klein-Gordon field

    I'm self-studying QFT and attempting exercise 2.2 on Peskin & Schroeder. First off, I'm a bit confused on the logic the authors use in the quantization process. They first expand the fields in terms of these ##a_{\vec{p}},a_{\vec{p}}^\dagger## operators which, if I understand correctly, is...
  9. patric44

    Quantum Need a book to explain the princple of quanization

    hi guys i am struggling to understand how and why quantization of energy solves the UV catastrophe and the black body problem ? and how they get to the Rayleigh - jeans equation in the first place ? and why plank modified the equation the way he did ? and why should the harmonic oscillators...
  10. Urs Schreiber

    Insights Mathematical Quantum Field Theory - Quantization - Comments

    Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Quantization Continue reading the Original PF Insights Post.
  11. Zahidur

    B Why did Max Planck quantize light?

    I've read up on the history of quantization and I can't seem to find a definitive answer on why Planck actually quantized light. Some sources say that he came up with the idea of energy being quantized in order to solve the blackbody problem, whilst others say that he was trying to create a more...
  12. N

    I If an object is not quantized does it have a wave function?

    Is there a relationship between the quantization of an object and its wave function? If an object isn't quantized does it have a wave function? For example, in string theory branes are not quantized, so do they have wave functions?
  13. redtree

    I Planck's constant and quantization of energy

    Given: ##\textbf{E}=\hbar \textbf{k}## where ##\textbf{k} = [\vec{k}_1, \vec{k}_2,\vec{k}_3, i c \omega]## If ##\textbf{k}## can vary continuously, how does the equation imply that energy is quantized? For example, ##y = m x +b## where ##m = \hbar## does not imply quantized ##y##. For...
  14. G

    Is energy transport in electric DC setup quantized?

    I have to say first that I found quite a similar question under https://www.physicsforums.com/threads/poynting-vector-dilemma.331375/ However those thread ended without real answer. There shall be the following simple setup: A battery, and quite at a distance a light bulb. They are connected...
  15. S

    I Calculation of vibronic couplings

    Hi all, I'm referring to the paper Chem. Phys. v.26 pp.169-177 y.1977 from Cederbaum, Domcke and Köppel where the expressions for linear vibronic coupling parameters are derived in second quantization notation. I'm stuck on the point, where the dependence of the fermionic ladder operators on...
  16. Ken Gallock

    B What kind of experiment is needed to quantize gravity?

    Hi everyone. I heard that there are several theories or hypotheses to quantize gravity such as superstring theory, loop quantum gravity, etc., and I believe none of them are conclusive (that's what I heard). So, here is my question. 1) Is it because there are no experimental results which prove...
  17. H

    A Canonical quantization of scalar fields

    In the srednicki notes he goes from $$H = \int d^{3}x a^{\dagger}(x)\left( \frac{- \nabla^{2}}{2m}\right) a(x) $$ to $$H = \int d^{3}p\frac{1}{2m}P^{2}\tilde{a}^{\dagger}(p)\tilde{a}(p) $$ Where $$\tilde{a}(p) = \int \frac{d^{3}x}{(2\pi)^{\frac{3}{2}}}e^{-ipx}a(x)$$ Is this as simple as...
  18. Aurghyadip Kundu

    Bending of Light in diffraction? Is it actually possible?

    I know light has wave particle duality, I understand these two points very well, 1. Light moves as a probability function, taking all the possible paths at once. The alternate paths cancel themselves out, resulting in a particle-like combined motion. 2. When relatively close to an edge, some...
  19. G

    How Fourier components of vector potential becomes operators

    Hello. I'm studying quantization of electromagnetic field (to see photon!) and on the way to reach harmonic oscillator Hamiltonian as a final stage, sudden transition that the Fourier components of vector potential A become quantum operators is observed. (See...
  20. T

    Second Quantization Density Matrix

    Homework Statement Homework Equations and attempt at solution I think I got the ground state, which can be expressed as |\Psi \rangle = \prod_{k}^{N}\hat{a}_{k}^{\dagger} |0 \rangle . Then for the density matrix I used: \langle...
  21. Isaac0427

    Planck scale

    Hi, So I am a little confused on the Planck scale. Correct me if I'm wrong (I hope this doesn't sound idiotic) but I believe that any field on a classical scale should be able to be quantized and work on a quantum scale/Planck scale, where the Planck length and the Planck time are the...
  22. Isaac0427

    What exactly is a field?

    Hi all! I'm only 12 but I am very interested in quantum physics. I do not have any resources at school to ask these questions, so I have to do independent research. As I didn't have a good background in physics, I had trouble understanding everything. So first of all I think I understand the...
  23. BiGyElLoWhAt

    Carrier particles and E-Field Propagation

    A thought experiment that is a consequense of a question someone asked in my particle physics class: We place an isolated electron. We wait 10 years, and place a half ring of electrons (spaced far apart from each other, but uniform) 10 LY away from our central e. Will our charges move? If so...
  24. W

    Quantization of EM field in dielectric?

    hi , what is the equation for the hamiltonian of EM field in dielectric and how can we say we have quantized the hamiltonian?