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.
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...
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...
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...
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...
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...
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...
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...
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...
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...
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?
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...