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. N

    I Symmetrized Lagrangian (second quantization)

    Hello, I need some help to find the correct symmetrized Lagrangian for the field operators. After some work I guess that $$\mathcal{L} = i[\overline{\psi}_a,({\partial_\mu}\gamma^\mu \psi)^a] -m[\overline{\psi}_a,\psi^a ]$$ should be the correct Lagrangian but I'm not sure with this. I'm...
  2. F

    B QM: Quantization Dependent on Spatial Confinement?

    Hello Forum, Some observables in quantum mechanics are always quantized, i.e. come in discrete separate values, while other observables, like energy or momentum, can be quantized or not depending on the spatial confinement of the system. Is that correct? Is spatial confinement of the physical...
  3. 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?
  4. K

    I Canonical Quantization: Choosing the Right Lagrangien

    Suppose we have a classical system described by a Lagrangien \mathscr{L}(x,t). The same system can be described by the Lagrangien \mathscr{L'}(x,t)=\mathscr{L}(x,t)+\frac{\mathrm{d}F(x,t)}{\mathrm{d}t}. where F(x,t) can be any function. If we now quantize the system by calculating the...
  5. V

    Solid State Books for second quantization and condensed matter

    Hi. I'll be doing a master's degree in nanophysics and working on electron transport in arrays of qubits. I don't know anything (or barely) about the second quantization and would like a book which covers it, and on condensed matter overall. So far I've been told about Bruus&Flensberg's...
  6. weezy

    I Bohr-Sommerfield quantization of motion

    From wikipedia I understand that the old quantum condition $$\oint_{H(p,q)=E} p_i dq_i = n_i h $$ states that not all kinds of motion are permitted in a system. My question is why is this called the old quantum condition and what is quantization of motion? Does this mean that a particle jumps...
  7. 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...
  8. 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 by...
  9. 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...
  10. S

    I Second quantization and creation/annih. operators

    I'd like some help with something in this introduction to second quantization ... http://yclept.ucdavis.edu/course/242/Class.html They start by considering two operators ##a## and ##a^\dagger## such that ##[a,a^\dagger]=1## and they are adjoint to each other. Also introduced is a state...
  11. Konte

    I Quantization of electromagnetic field

    Hello everybody, It is known that electric field operator is shown as \hat{E}(r,t)=-i\sum_{k,\lambda}\sqrt{\frac{\hbar\omega_k}{2\epsilon V}}\left(a(t)^\dagger_{k,\lambda} e^{-ik.r} - a(t)_{k,\lambda} e^{ik.r} \right) \hat{e}_{k,\lambda} But if I need to represent an electrostatic field in a...
  12. 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...
  13. 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...
  14. D

    DSP - Rounding and Truncation Quantization

    Homework Statement Homework EquationsThe Attempt at a Solution Alright, so far what I know about Digital Signal Processing is that you first sample the values of the signal with infinite precision/infinite amplitude values and of course you can't encode these values, so you need to...
  15. B

    I Energy quantization of the particle in a box

    I'm self-learning quantum mechanics and I'm reading the famous Shankar book (Principles of Quantum Mechanics - second edittion). At page 161 of the book, I don't understand the following part of this page: "Let us restate the origin of energy quantization in another way. Consider the search...
  16. 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...
  17. V

    Has the Charge Quantization Problem Been Solved Without Magnetic Monopoles?

    I am no mathematician, not even an expert in Gauge Theories, but I came across this article http://arxiv.org/abs/1409.6716 (published here http://www.sciencedirect.com/science/article/pii/S0393044015002284) when I was looking for some "condensed-matter-type-monopoles", and the author claims...
  18. Qturtle

    Quantization of classical strings - a beginner's question

    Hey all. I've started to read and watch lectures on string theory. usually everyone starts with a classical relativistic particle action, and then goes to a classical relativistic string action. after they finish with the classical string they start the quantization process. my question is...
  19. I

    Quantization Explained: Understanding Photon Energy Packages

    Hi, I'm having a hard time understanding what exactly it means to be quantized. I know that electromagnetic radiation is quantized, and that means coming in little "packages" of energy, I can't really wrap my head around this, and would like if someone could explain this a better way maybe...
  20. S

    Canonical Quantization: Explaining the Covariance Paradox

    Hi all I am studying Quantum Field Theory. I read the following statement :"Canonical quantisation is intrinsically not relativistically covariant. Can anyone explain why?. Although everything we did from the beginning was lorentz invariant! Thank you .
  21. yeshuamo

    Kinetic energy of electron: Quantization of angular momentum

    Homework Statement Show that the quantization of angular momentum implies that the kinetic energy of the electron is quantized as K=nhforb/2, where forb is the frequency of rotation. Assume circular orbit. Homework Equations Radial acceleration: arad = v2/r = (4π2r/T = 2*π*v/Tr = nħ KE =...
  22. stevendaryl

    Second Quantization vs Many-Particle QM

    Apparently, there are two different routes to get to quantum field theory from single-particle quantum mechanics: (I'm going to use nonrelativistic quantum mechanics for this discussion. I think the same issues apply in relativistic quantum mechanics.) Route 1: Many-particle quantum mechanics...
  23. 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...
  24. 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...
  25. S

    Second Quantization Tight Binding Model of Rashba Spin-Orbit

    Resolved. (not sure how to delete the entire post)
  26. Andre' Quanta

    First quantization light ray in Schwarzschild's black hole

    The dinamic of a light ray in a Schwarzschild' s metric is governed by a lagrangian where the potential is V(x)= a*(1/r)^2-b*(1/r)^3 with a and b positive costants. The presence of a Lagrangian it means that is possible to apply a first quantization of this sistem; if so which are the...
  27. Andre' Quanta

    Quantum Spectrum of a Hamiltonian with Linear Potential

    Suppose to have a hamiltonian with a linear potenzial like z x, where x is the variable and z a parameter. Which is the spectrum of the Hamiltonian of this sistem?
  28. Isaac0427

    Understanding the 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...
  29. Isaac0427

    Is Every Physics Equation 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...
  30. P

    Logical explanation for quantization

    Why are things quantized? Just say for example that energy increases continuously. If this is true, than objects would accelerate to infinite speeds when falling to Earth because they are falling through an infinite amount of equipotential surfaces, all with values equal to 9.8. And an...
  31. Z

    Canonical quantization of spin-3/2 particle

    If I want to calculate a decay of excited nucleons,sometimes I must treat the spin 3/2 field operator. If I use CG coefficient method, for example http://arxiv.org/abs/hep-ph/0210164 (page 3,the third equation) But it is a result,not the starting.The thought looks like a synthesis between...
  32. K

    Quantization of Earth's angular momentum

    Homework Statement If the angular momentum of Earth in its motion around the Sun were quantized like a hydrogen electron, what would Earth's quantum number be? How much energy would be released in a transition to the next lowest level? Would that energy release be detectable? What would be the...
  33. Pranav 10

    Hi I want to know about quantization of electricity?

    1.Is Quantization of electricity is helpful for increasing Voltage? 2. Can I use galvanometer in capacitor to increase it's capacitance? Thank u , I am new to this forum.I want to ameliorate my knowledge in electrical engineering.
  34. dextercioby

    Does quantization always work?

    Of course it doesn't. But let me see if I can bring an argument on how some (perhaps elementary) things are so tricky, that their textbook treatment is almost absent. The axiom of QM which (for some unknown reasons) is least emphasized is this one: <For a quantum A system made up of...
  35. A

    Bohr Quantization with linear potential

    Homework Statement Using Bohr's quantization rule find the energy levels for a particle in the potential: $$U(x) = \alpha\left|x\right|, \alpha > 0.$$ Homework Equations ##\oint p\, dx = 2\pi\hbar (n + \frac{1}{2})## The Attempt at a Solution Okay so: ##\begin{eqnarray} \oint p\, dx &= \int...
  36. 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...
  37. E

    Quantization of EM in UV & vacuum

    UV catastrophe didn't occur because em are quantized.. so the higher frequency modes were not there. In vacuum.. if you compute the contribution of the em modes, it is 120 magnitude greater than observed.. the mystery is why it is not and they theorize it is just canceled out. But why didn't...
  38. W

    Field Quantization: Raising & Lowering Operators

    hi, i studied the field quantization in terms of raising and lowering operators , in its derivation we consider cavity- my question -a) Is field consider to be quantized in cavity only ? b)how do we link mode of electromagnetic field with harmonic oscillator ?
  39. naima

    Electromagnetism Quantization

    I start from these formulas(transverse electric and magnetic fields) ## E_\perp(r) = \Sigma_i i \mathscr E_{\omega_i}\epsilon_i [\alpha_i e^{i k_i . r}- \alpha^\dagger_i e^{-i k_i . r}]## and ##B(r) = \Sigma_i i(1/c) \mathscr E_{\omega_i}(\kappa_i \times \epsilon_i) [\alpha_i e^{i k_i . r}-...
  40. 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?
  41. P

    Using Bohr quantization rules to calculate energy levels

    Homework Statement Use the Bohr quantization rules to calculate the energy levels for a particle moving in a potential \begin{equation} V\left(r\right)= V_0 \left(\frac{r}{a}\right)^k \end{equation} where k is positive and very large. Sketch the form of the potential (done) and show that the...
  42. A

    Why Quantization? Elucidating Wave Nature of Particles

    Is quantization a consequence of the wave nature of particles? Elucidate.
  43. D.R.U

    Quantization & Discontinuity in Physics: Possible?

    What is your thought s about quantization and discontinuity in physics...is possible?...if yes then How?
  44. marcus

    Deformation quantization (survey, introduction, sources)

    In case anyone is interested in DQ I came across this, which is moderately accessible in parts. http://math.berkeley.edu/~alanw/242papers99/karaali.pdf Evidently Alan Weinstein (Berkeley faculty) was teaching a graduate course Math 242 back in 1999 and put this online for his students. If...
  45. Uday

    A Doubt Regarding Quantization of charge ,its relevance in integration

    a) We know that the smallest charge that can exist is 'e' . But in several instances (such as calculating potential energy of sphere of charge ) we consider 'dq' and then integrate it . How can we justify this ? b) We know that 1/2 or 1/3 of e (charge of electron) doesn't exist . But...
  46. michael879

    Quantization of Angular Momentum Under Boosts

    Is the spin of an electron still \hbar/2 in the direction transverse to its momentum? Classically angular momentum transforms non-trivially under boosts, so I was wondering if this applies to quantum mechanics too. A more general question would be: Is angular momentum quantized into units of...
  47. WannabeNewton

    Where Can I Find the Older Printing of Greiner's Field Quantization Book?

    Greiner "Field Quantization" https://www.amazon.com/dp/3540780483/?tag=pfamazon01-20 I really, really want to buy this book. However, the amazon reviews seem to echo the statement that the margins in the newest printing are completely screwed up and actually make reading the book painful...
  48. M

    Quantization Rule for Planetary Motion?

    according to sommerfield quantization rule "for any physical system in which the co ordinates are periodin functions of time,there exist a quantum condition for each coordinate(e.g in bohrs heory angular momentum is quantised)" then why there is no quantization rule in planetary motion but the...
  49. M

    Quantization of the Electromagnetic Field

    We have recently begun learning about quantization of the electromagnetic field and I would to understand more. It is tempting to want to connect the number states of a definite momentum and polarization to the concept of a classical plane wave. However it seems less straightforward than I might...
  50. G

    What is the first and second quantization?

    I believe the title says it all. What is the first and second quantization? What is the difference? Thank you.
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