Questions tagged [discrete]

Discrete means as opposed to continuous. For, instance, people may ask questions about discrete electric charges, discrete spacetime, discrete energies, etc. If discretization is vital/essential to the question then tag it with the [tag:discrete] tag.

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How does angular momentum get quantized? [duplicate]

We know that the magnitude and direction of angular momentum is quantized in quantum mechanics. We can explain the quantization with the help of quantum numbers. But actually who is responsible for ...
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Uniform discrete physical theories [closed]

I'm looking for a list of physical theories which are discrete and uniform (in some sense). For example, if space-time has a regular lattice like structure this would be uniform. If possible, are ...
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862 views

Generator for parity?

The unitary translation operator, $\hat{T}(\lambda) = e^{i\hat{p}\lambda/\hbar}$, is generated from the Hermitian operator $\hat{p}$. The unitary rotation operator, $\hat{R}_z(\alpha)=e^{-i\hat{L_z}\...
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Is the Planck length a minimum or a unit of discrete distance? [duplicate]

Can 2 things, or 2 measured distances be 1.2 planck lengths away from each other? Or must they be 2 planck lengths away?
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Why is the optimum window length for a discrete fourier transform of a signal less than 100%?

I'm trying to determine the best settings for a discrete Fourier transform on a signal with noise. Now I've stumbled on something that I can't seem to explain, I'm hoping someone can give me some ...
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2answers
55 views

Density Of states derivation

In the aspect of density of state derivation or simply assuming the frequency of a solid as a continuous distribution we have to come up with an equation expressing the density of states. Its derived ...
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1answer
26 views

Partition Function when the Energy States are Both Discrete and Continuous

Normally for statistical mechanics (in this example I will be only refering to the canonical formalism to keep things simple) we generally have a system that we solved the equations of motion for and ...
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93 views

Is force quantised?

Things like charge, distance, energy, etc are quantised , Are all the phenomenon around us also quantised ?? Like time or say Force !? I was reading this question which goes about seeing the effect ...
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22 views

Update: Does the Planck scale imply that spacetime is discrete? [duplicate]

This question has already been asked Does the Planck scale imply that spacetime is discrete? however I'm wondering if there has been any change in the community since it was asked roughly 8 years ...
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Why is photon quantized in vacuum? [duplicate]

Apparition of quantized energy levels in quantum physics is usually explained in analogy with sound waves in a box (like in music instruments): the wave has to satisfy the boundary conditions and ...
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19 views

Fourier transform of some discrete, finite, non-uniform signal

Suppose I have some finite signal $x(t)$ of $N$ data points. This signal is produced by some program or some experiment and so is discrete and the difference in time between each data point $\delta t$ ...
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1answer
55 views

Problem in the continuum limit of a Kronecker delta

I am having troubles in understanding how to correctly perform the continuum limit of a double sum containing a Kronecker delta. Imagine to integrate a function depending on $t$ and $t'$, both ...
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1answer
28 views

Discrete energy rounding

If energy is only found in discrete amounts what happens when the amount of energy falls below the minimum individual unit? does it have a floor or ceiling function or does it matter what type it is?
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Discrete energy levels of electrons in isolated atom

My question is a duplicate of this. Please consider the equation $\nabla^2\psi + (2m/\hbar^2)[E-V]\psi=0$ (1) Potential of electron revolving hydrogen atom is given as $V=\frac{-e}{4\pi\...
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Is the whole electromagnetic spectrum made of quanta?

My question is probably stupid (and maybe has already been answered on other posts), but I just started investigating quantum physics and I am struggling to understand the real meaning of "quantum". ...
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Why light coming from distant stars is not discrete? [duplicate]

Imaging the light racing out from distant sun, as beam of light shoots aways is a circular pattern (spherical actually), remembering that, light comes in photons or packets of energy. so how come is ...
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1answer
77 views

Where exactly does energy quantisation come in for light?

Planck quantised the energy of light in order to solve the black body radiation problem. However, I am confused as to exactly what he quantised. On one hand, I have seen that he quantised the energy ...
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42 views

Discrete time evolution in a non-Euclidean space?

The time independent schrödinger equation can be written as $$i\frac{\partial \psi}{ \partial t}=H\psi$$ if we consider the case of a 1D particle we can evolve it in time by discretising the ...
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Can Noether's theorem be applied to cyclic time symmetries? [duplicate]

Noether's theorem relates continuous symmetries in the time evolution of a system to a conserved value. Many conserved values, such as conservation of momentum, can be described via this theorem. I'...
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Is the answer to the question “How many moments in time exist between any two particular moments?”, infinitely many? [duplicate]

This question is related to Xeno's paradox, and to the discrete/continuous time debate, but it comes from a slightly different angle. If the answer is infinitely many, why would this not be a ...
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Geometrical way to view discretization of energy in quantum mechanics. How commutation relation implies discreteness?

The relation from which discreteness in eigenvalue of the energy of bound state arises is $[x, p]=i\hbar$ followed by the rule that wavefunction should be normalizable. So my question is there a ...
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1answer
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Would any continuous model of the universe have/be based on hypercomputational laws?

I've read that when Turing-Church thesis is applied to the universe and physics, one of the three interpretations that we can use and is defended by some important physicists is that: "The universe ...
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1answer
68 views

Discretization of Hamiltonian with first derivative

In a particular 1D system, the Hamiltonian can be writen as $$H=\mathrm{i}\left(f(r)\frac{\partial}{\partial r}+\frac{1}{2}f'(r)\right)\; ,$$ wher $\mathrm{i}$ is the imaginary unit, and $f(r)$ is a ...
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3answers
169 views

Superposition principle forbids quantisation?

Apparently bound states in quantum mechanics require energy states to be discrete. That means energy in such systems is quantized, right? However, say that we have a superposition of energy ...
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1answer
116 views

Is entropy quantized in Loop Quantum Gravity?

From the Beckenstein-Hawking formula, we know that entropy is proportional to the area of the event horizon of a black-hole: $S\propto A$. From Loop Quantum Gravity, we know that length, area and ...
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110 views

Quantization of electrons' angular momentum in atoms and molecules

It is known that the Schrödinger's equation of the electron's wave function in atoms can be solved analitically only when a single electron is present (the "hydrogenlike atom"). In that case, the ...
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1answer
89 views

How to Find Jerk from Discrete Velocity Data?

I have measured the velocity of an object at discrete intervals. I want to find the corresponding acceleration and jerk of the object. How do I do this with discrete values rather than continuous ...
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1answer
98 views

Is space continuous? [duplicate]

Take a particle, it has a position $(x, y, z)$ maybe it is $(0.231, 8.962, 10.567)$. Is there a maximum precision to this? Is the space discrete or continuous? If it is discrete, how thin the ...
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20 views

What is the flux $\Phi$ enclosed by cyclotron orbit, which can express the quantization rule?

Suppose an electron (mass $m$, charge $e$) in the xy-plane with $B=(0,0,B)$ (The classical EOM result in circular orbit). Using the Bohr-Sommerfeld quantization rule we can find that $E_n = (n+1/2)\...
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69 views

Compactness and Quantization

So I was thinking today about when observables become "quantized", and came to the conclusion that every instance of quantization I've ever come across has come about from solving the Schrödinger ...
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3answers
68 views

What are wave-functions in QM. corresponding to?

I was learning about a particle trapped in a double well potential $$V(0) = \infty, V(x1)=\infty$$ which can be described by $\psi_n$ for n=0,1,...,$\infty$ with corresponding Energies $E_n$. Just ...
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21 views

Aggregation phenomena : How to get from a discrete to a continuous point of view

I'm studying a diffusion limited aggregation phenomenon. The $N$ particles diffuse in a box and when there is a contact they stick with a probability $p$, and let's say to simplify $p=1$. Meaning that ...
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1answer
56 views

Minimal Requirements for Space and Time

I read recently that to consider the Planck length of less than 1.6 x 10 exp -34 meters the smallest unit that can manifest 4 coordinate space time to be incorrect in its interpretation. The reason ...
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Is it possible to define background independent fluid dynamics equations?

Imagine a lake, and you measured the distance from each molecule to it's neighbours for molecules to within say 3 molecular radii. Taking this data you could reconstruct the positions of the ...
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4answers
156 views

Is it possible to have non-integral multiple of $e$ as charge?

We have 2 similar balls. On one ball there is charge $e$ and on other no charge. I connect the balls using a metal wire. We know that the charge gets shared until they have the same charges. Thus we ...
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98 views

Why any theory of spacetime atoms would be wrong from start? What about causal sets?

After watching this public talk by Nina Arkani-Hamed titled "The doom of spacetime", I can't fully understand what he said in the answer to an audience question about gravity. He said we can't simply ...
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106 views

Can Probability be quantized? [duplicate]

There are conjectures that quantities like space, time, energy, etc. are quantized and can only get some discrete values. I was wondering if there is any relationship in physics that interrelates ...
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2answers
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IQHE, quantized conductance, and zeeman splitting

I've been trying to understand IQHE by reading these lecture notes by David Tong. Mainly, I was trying to understand the quantized hall resistivity in terms of the number of Landau levels crossing ...
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23 views

Does our universe has a limited decimal precision? [duplicate]

This question may be a bit strange but I was wondering if our universe has a kind of limit in precision. For example: A particle can be in coordinates a or ...
3
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4answers
127 views

In $E=hf$, can $f$ assume any positive value? (Beginner) [duplicate]

The energy of photon is given by the equation $E=hf$, where $h=$ Planck's constant, and f=frequency of radiation. Is f quantized, or can it assume any value? If it can assume any value, then wouldn'...
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2answers
135 views

Why position and momentum operators are both continuous spectrum while angular momentum is discrete? [duplicate]

We know that position $\hat{r}$ and momentum $\hat{p}$ are both continuous spectrum operators, i.e. $$\hat{r}|r'\rangle=r'|r'\rangle, \quad \hat{p}|p'\rangle=p'|p'\rangle.$$ But the angular operator $\...
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3answers
106 views

What was shocking in Einstein's partcile theory of light?

I know that when Einstein proposed the particle theory of light it was revolutionary and shocking for most of physicists and it took years to accept that view. Particle theory had been proposed in the ...
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2answers
87 views

Do we know, or at least have a strong argument for the fact that for a given time interval, we can always find a smaller time interval? [duplicate]

Motivation: In Biology, when, for example, biologists try to model the population dynamics of a population, they say: Let $N: \mathbb{R}^{nn} \to \mathbb{R}^{nn}$ be a function that represents ...
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69 views

Could spacetime have crystalline properties?

Space-time is currently modeled as a continuous manifold. However, space-time shares many features in general relativity that mimic a fluid-like thing. Fluids are certain states of matter and under ...
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74 views

Non-vanishing matrix elements in QFT after discretization

In QFT, introducing the lattice size $L$ implies that the momentum of plane wave solutions is discretized as $$\vec{p}_\vec{n} = \dfrac{2\pi}{L}\vec{n}\quad,\qquad \vec{n}\in\mathbb{Z}^D$$ I would ...
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2answers
366 views

Is Bohmian mechanics wrong in the case that space and time are quantized?

Bohmian mechanics assumes that particle trajectories are continuous. Also, it claims the random outcome of certain experiments (like the double-slit experiment) to be due to the random initial ...
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Why the eigenvalues of hamiltonian are discrete in bounded systems (only discrete energy levels)? [duplicate]

In one dimensional motion the general potential is given as in the figure above When energy is between V min and V 1 the energy levels are discrete like in the potential barrier and well example or ...
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2answers
255 views

Why atom has the straight discrete energy levels? [duplicate]

Interaction between a nucleus and electrons is in gravity(not considering) and electrostatics. Due to electrostatics nucleus attracts electrons. The force that describes this process is $$F=k\dfrac{...
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22 views

Pairwise additivity of numerical potentials

Surely this is a trivial problem, but I'm very much confused on how to approach so please bear with me. Say I have a two-dimensional evenly-spaced 16x16 grid centered at the point (x1,y1). I also ...