# 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. ### I When was the formula for the Stern-Gerlach experiment found?

Today we know that if you make successive Stern-Gerlach measurements the beam of atoms will split according to this formula: > cos^2 (theta/2) And this is something people back then could have figured out, they could have done many measurements, plotted the values, and realized it followed...
2. ### I Prefactor in Canonical Quantization of Scalar Field

Hey all, I am encountering an issue reconciling the choice of prefactors in the canonical quantization of the scalar field between Srednicki and Peskin's books. In Peskin's book (see equation (2.47)), there is a prefactor of ##\frac{1}{\sqrt{2E_{p}}}## whereas in Srednicki's book (see equation...
3. ### Non quadratic potentials and quantization in QFT (home exercise)

I noticed that ##V(\phi)## has nonzero minima, therefore I found the stationary points as ##{{\partial{V}}\over{\partial\phi}}=0##, and found the solutions: $$\phi^0_{1,2}=-{{m}\over{\sqrt{\lambda}}}\quad \phi^0_3={{2m}\over{\sqrt{\lambda}}}$$ of these, only ##\phi^0_3## is a stable minimum...
4. ### I Canonical quantization of Ashtekar's new variables

Is Loop quantum gravity canonical quantization of Ashtekar's new variables correct ? if not in principle is there any particular ways to canonical quantization of Ashtekar's new variables ? are there other methods to quantization of Ashtekar's new variables ?
5. ### Space-time quantization and its philosophical aspect

Modern physics describes matter by real numbers. This means that an absolutely accurate description of any particle requires an infinite amount of information. Intuitively, it seems that this should not be so, and the model of the Conway's Game of Life looks more close to reality. In this...
6. ### A Coherent quantization, the non-unitary case

This is a question specifically for @A. Neumaier ! At Peter Woit's blog, Arnold commented about his formalism for quantum mechanics, coherent quantization. I left a question but Peter Woit doesn't always let comments through, so, here is the question: Why aren’t you restricted to unitary...
7. ### I Quantization of the electromagnetic field

Hi everyone, It is about the quantization of the electromagnetic field. The expression of field E and B are defined with: -the annihilation a- and creation a+ operators, and the frequency ω. So my question is: how does these fields must be expressed if they where "static"? I mean, how the...
8. ### A Hamiltonian in second quantization

Hello ! I require some guidance on this prove :I normally derive the Hamiltonian for a SHO in Hilbert space with a term of 1/2 hbar omega included. However, I am unsure of how one derives this from Hilbert space to Fock space. I have attached my attempt at it as an image below. Any input will be...
9. ### A What is the point of geometric quantization?

I studied the basics of geometric quantization for a recent work in quantum-classical hybrid systems1. It was an easy application of the method of gometric quantization (prequantization + polarization in ##\mathbb{R}^{3}##). The whole topic seems interesting since I want to learn more of...
10. ### I Bohr-Sommerfeld quantization

Recall that in the semi-classical Bohr-Sommerfeld quantization scheme from the early days of quantum mechanics, bound orbits were quantized according to the value of the action integral around a single loop of a closed path. Clearly this only makes sense if the orbits in question permit closed...
11. ### 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...
12. ### B Understanding Light Quantization

Hi, I'm still unclear on the quantization of light. I watched this 1m video called "Why Light is Quantum" - Why Light is Quantum by minutephysics. The author says light has the same energy distribution as a gas? What does this mean? What is an example of the energy distribution of a gas...
13. ### A Second Quantization in QFT

In Quantum Field Theory and the Standard Model by Schwartz, he defines the Hamiltonian for the free electromagnetic field as (page 20, here's a link to the book). This follows (in my understanding) from the fact that the amplitude of the field at a given point in space oscillates as a simple...
14. ### I Wilson-Sommerfeld quantization to solve square-well potential

The Wilson-Sommerfeld quantization rule claims (##\hbar=1##) $$\frac{1}{2\pi} \oint p(x)\,dx=n,\,n=1, 2, ...$$ where integration is done in the classically allowed region. Applying this to a square-well potential with a depth of ##V_0## and width ##a##, we get $$E=\frac{\pi^2 n^2}{2a^2}$$ This...

Summary
16. ### B Fundamental particles and mass quantization

We know that the energy levels for electrons surrounding nucleus are quantized , only coming in discrete levels. When I see the standard model of elementary particles table I notice specific masses for each of the particles whether they be quarks or leptons or bosons like the higgs. I know that...
17. ### B Where is the quantization term in Planck's Law?

This is a very remedial question, so thanks in advance for you gentle indulgence :smile: Where do I find the quantization term (the "n") in Planck's Law?

19. ### A Dirac Field quantization and anti-commutator relation

Can anyone explain while calculating $$\left \{ \Psi, \Psi^\dagger \right \}$$, set of equation 5.4 in david tong notes lead us to $$Σ_s Σ_r [b_p^s u^s(p)e^{ipx} b_q^r†u^r†(q)e^{-iqy}+ b_q^r †u^r†(q)e^{-iqy} b_p^s u^s(p)e^{ipx}].$$ My question is how the above mentioned terms can be written as...
20. ### 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...
21. ### 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...
22. ### I Relationship between Planck Distribution and Quantization of Energy

I came to understand that Planck Distribution is necessary to explain UV catastrophe. With that necesity in the background, the distribution equation eventually suggests that the energy emitted by black body has discret values. But I wonder how that's related to E=nhv. I understand that "n" also...
23. ### A Is the Klein-Gordon equation a quantization of classical particles?

The Schrödinger equation can be derived from the path integral quantization of the Lagrangian of classical, non-relativistic particles. Can the Klein-Gordon (and maybe the Dirac) equation be derived from the path integral quantization of a given classical (supposedly relativistic) Lagrangian of...
24. ### Second Quantization - Quasiparticles

(Simplified version of Baym, Chapter 19, Problem 2) Calculate, to first order in the inter-particle interaction V(r-r'), the energy of an N+1 particle system of spin-1/2 fermions with on particle of momentum p outside an N-particle Fermi sea (quasiparticle state). The answer should be expressed...
25. ### 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...
26. ### Book recommendations for second quantization and Jellium model

please refer me a good book for the detail step by step study on the second quantization. and also where can I find the jellium model for the metal?
27. ### Help with second quantization practice problem

Hi, to help further my understanding of the second quantization for one of my modules I would like to show that the following expressions $$\hat{H} = \Sigma_{ij} \langle i| \hat{T} | j \rangle \hat{a_i }^{\dagger} \hat{a_j}$$ $$\hat{\psi}(r,t)= \Sigma_k \psi_k(r) \hat{a}_k(t)$$ Obey the...
28. ### A Quantization of the electric field inside a box

Hello all, The second quantization of a general electromagnetic field assumes the energy density integration to be performed inside a box in 3D space. Someone mentioned to me recently that the physical significance of the actual volume used is that it should be chosen based on the detector used...
29. ### Canonical Quantization: Steps to Find iħ

Homework Statement For the canonically quantized operators, what are the step in between? how do you get the answer iħ? [q^,p^]=iħ q^ is the coordinate and p^ is the momentum.
30. ### 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...
31. ### 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...
32. ### Bosonic operator eigenvalues in second quantization

Homework Statement Following from \hat{b}^\dagger_j\hat{b}_j(\hat{b}_j \mid \Psi \rangle )=(|B_-^j|^2-1)\hat{b}_j \mid \Psi \rangle , I want to prove that if I keep applying ##\hat{b}_j##, ## n_j##times, I'll get: (|B_-^j|^2-n_j)\hat{b}_j\hat{b}_j\hat{b}_j ... \mid \Psi \rangle . Homework...
33. ### I Understanding second quantization

Hi, I was reading a book about second quantization and there were a few things that I didn't quite understand entirely. This is what I understood so far: Given an operator ##\mathcal A## and two orthonormal bases ##|\alpha_i\rangle## and ##|\beta_i\rangle## for the Hilbert space, ##\mathcal...
34. ### A What is the difference between second quantization and QFT?

Please teach me the difference between second quantization and QFT?
35. ### Coulomb's Law and charge quantization

Coulomb's law states that the force between particles depends on their charge. But protons and electrons have equal but opposite charges. Shouldn't the formula simply have constants with the only changes required being the signs?
36. ### 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...
37. ### I What is the origin of quantization?

What is the origin of quantization? For example, electron of hydrogen atom has quantized energy level. But free particle has continuous energy level. Interaction with another particle or any potential acting on particle makes such quantization?
38. ### A Field quantization and photon number operator

[Moderator's note: This thread is spun off from a previous thread since it was getting into material too technical for the original thread. The quote at the top of this post is from the previous thread.] Field quantization doesn't require a photon picture. A measurement device that creates a...
39. ### I Why the second quantization Hamiltonian works?

I am puzzled by the fact that a "single-particle" Hamiltonian (in the annihilation and creation operator form) may be used for a multi-particle case (non-interacting particles) or that (only) a "two-particle" Hamiltonian (in the annihilation and creation operator form) may be used for a...
40. ### 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...
41. ### 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.
42. ### B Quantization & Indetermination

Hello, Is the quantization of the action the origin of the indetermination? The reasoning goes like this: - Just talking abut one example, a single particle with position and momentum - keep it simple - - The measure of the position could have any value, in principle - The same for the...
43. ### I Dirac quantization of gravity e.g. GR in Ashtekar Variables

I'd like this issue clarified I understand that a full nonpertubative quantization of a yang mills gauge theory in 4D is unavailable. is Dirac quantization of classical theory of gravity e.g GR rewritten Ashtekar Variables Variables or some variation of the idea, a viable approach to a...
44. ### I Canonical Quantization: Proving the Theory

Hello! I read some books on QM and QFT but I didn't really noticed (or I missed it?) a proof for the canonical quantization. For example, for energy and momentum it makes sense to have opposite signs, due to Minkowski metric, be related to the variation of space and time, due to Noether theorem...
45. H

### B Time quantization in classical physics

Hello, It is considered that the time is continuous in classical physics, but it sounds paradoxal to me, let me explain. Let a particle inside a galilean frame of reference. This particle can only be measured either at rest, either in motion, but never simultaneously at rest and in motion...
46. ### I M-theory and loop quantization of higher dimensional SUGRA

A new duality between Topological M-theory and Loop Quantum Gravity Andrea Addazi, Antonino Marciano (Submitted on 17 Jul 2017) Inspired by the long wave-length limit of topological M-theory, which re-constructs the theory of 3+1D gravity in the self-dual variables' formulation, we conjecture...
47. ### I Single-mode field quantization Hamiltonian

Hi! I'm having some trouble on understanding how the Hamiltonian of the e-m field in the single mode field quantization is obtained in the formalism proposed by Gerry-Knight in the book "Introductory Quantum Optics". (see...
48. ### 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...
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### B Quantization of energy and ultraviolet catastrophe

How can the quatization of energy solve the ultraviolet catastrophe? I tried explanation on internet and on the book but i found nothing, can you help me?
50. ### I Understanding the scalar field quantization

I am getting started with QFT and I'm having a hard time to understand the quantization procedure for the simples field: the scalar, massless and real Klein-Gordon field. The approach I'm currently studying is that by Matthew Schwartz. In his QFT book he first solves the classical KG equation...