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 this tag.

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Can we describe 4 dimensional spinors on an 8 dimensional manifold?

I was reading about models of space-time, in particular where it is modelled as a mesh and that it becomes smooth 4D space-time in the limit as the cell sizes go to zero. (An example of this, is what ...
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Ising model correlation function in the high temperature limit

I'm reading the book 'Gauge Fields and Strings' by A. Polyakov and I don't understand his derivation of the correlation function of the Ising model in the high temperature limit. I don't really ...
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When we say a rigid body is a system of particles, what exactly are 'particles' here?

In Newtonian mechanics, a particle (in my knowledge) is a point-like mass with no shape and size, deformation, rotation and internal movements, which is an idealized model of an object which does have ...
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Propagator for a single particle in 1D in Polyakov's Gauge Fields and Strings

I was reading the book 'Gauge Fields and Strings' by A. Polyakov and I don't understand a step in the 1D single particle propagator derivation.. The part I don't understand is Eq. (1.2). for the ...
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How do I approximate an angular acceleration vector from a history of orientations?

A rigid body is simulated to move in six degrees of freedom. At every past timestep, I know its displacement vectors $x^{GLOB}$ in the global coordinate frame, as well as 3x3 matrices $R$ that ...
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2 answers
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Are there any significant integer constants that are not unitless? [closed]

When it comes to meaningful integer constants, the only ones I can come to think of (except zero) are unitless, for example 1 (the multiplicative identity), 2 (the base of the binary system), 10 (the ...
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Does the quantisation of energy apply to everything? [duplicate]

Radiation is quantised according to Planck, so that's out of the question. However, I have seen many simplifications that claim Planck introduced quantised energy. Period. Has Planck really done that? ...
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Discrete Spectrum vs Continuous Spectrum and Bounded, Scattering States

Apolgies in advance if this is a confusing ramble and multitude of questions, I'm not quite sure how to articulate myself. I am currently reading up on quantum mechanics and seem to have confused ...
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1 answer
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How to understand crystal momentum, its relation to translational symmetry, Noether theorem, and to symmetry breaking/Landau-Ginzburg theory?

This question continues from my another question How to understand critical points of the Brillouin zone, (in)direct bands of transition-metal dichalcogenides?, and is related to Is crystal momentum ...
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2 answers
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Quantization of Electric Charge and Cutting Spheres

Say you have a metallic sphere that holds a charge $Q$ uniformly. If we cut the sphere into two equal halves, each half of the sphere will hold a charge of $Q/2$. Also, electric charge is quantized. ...
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Can finite element analysis predict whether flow is turbulent?

Finite Element Analysis in Simulation Software to predict the Reynold's number are computed using the formula$=pVD/u$ or there is a finite element method for this? I was just wondering whether it ...
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Discretization of derivative of delta function and affine Kac-Moody algebra

In equation (4.16) of https://arxiv.org/abs/1506.06601, a discretization of the (classical) affine Kac-Moody algebra is presented: $$ \frac{1}{\gamma}\left\{J_{m}^{1}, J^2_{n}\right\}=J_{m}^{1} J_{n}^{...
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The uncertainty principle and the quantization of electron momentum in orbitals - Why are larger energy gaps considered more uncertain?

I am a chemist trying to understand how the uncertainty principle can be applied to the mechanics of atomic and molecular orbitals in order to have better intuitions about stability and reactivity. ...
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Rigorous treatment for continuous mass systems

I would like to ask if anyone knows an accessible, yet rigorous way of passing from a discrete system of mass-points to a continuous mass system. For instance, we clearly know how to define the ...
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1 answer
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Why a body can't have net charge in fraction of a Coulomb?

Q. Quantisation of charge implies:- (a) charge cannot be destroyed (b) charge exists on particles (c) there is a minimum permissible charge on a particle (d) charge, which is a fraction of a ...
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2 answers
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Space-time continuum expansion

I still don't understand how the expansion of the universe works. If the universe is made up of an infinite number of points that make up space-time, then how can space expand or stretch. Common sense ...
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Why do we need to make sense of QED in continuous spacetime anyway?

QED is an approximate description of reality. Even if it did give finite predictions in the continuum limit, those predictions would've been incorrect anyway! Newtonian gravity does give finite ...
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Discrete and continuous basis in Quantum Mechanics

In the context of Quantum Mechanics and Hilbert spaces, I understand that a function can be interpreted as $\psi(x) = \langle x \vert \psi \rangle$ in the position basis, and things like $$\int_a^b|\...
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Microstate and Phase space

Pathria, Statistical mechanics, 4ed,pg32-33 "The microstate of a given classical system, at any time, may be defined by specifying the instantaneous positions and momenta of all the particles ...
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Is charge not quantized fundamentally and that is why we haven't come across magnetic monopole?

If protons are getting charged from quarks.. then the charge in quarks is fractional and not quantized. Does this mean that the charge we see is not fundamental? And the charges in quarks are just ...
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-5 votes
2 answers
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Is time continuous or discontinuous? [duplicate]

As I notice I sometimes feel as if time is discontinuous it’s like a comic book where each act is planned out and the main character just comes there. Please give an explanation and correct me if I am ...
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How should I interpret the eigenvalues of a momentum operator discretised with a central-difference scheme?

I have a simple 1D momentum operator $P = -i\frac{\partial}{\partial x}$. I discretise it on a grid with spacing $h$ with a central-difference scheme like so: $\left[PF\right]_{x=jh} = \left[\mathbf{P}...
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How to transform from a discrete to integral equation?

In this picture, the red curve is an elastic rod that has resistance to bending and extension. I am trying to model the adhesions (contact) between the rod and the substrate (glass): the green dashed ...
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5 answers
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Is motion un-observable? and if so how can we know it exists?

Let's say I show you two pictures of the same desk, the only difference between them being the position of a red pen. Our intuition tells us that the pen must have been in motion at some point after ...
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Is there any good source talking about the quantization of time?

I am doing a little search about the quantization of time, but I didn't find anything explaining it in a conceptual or in a philosophical way? Is there anyone who can help?
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Discreteness of spectrum of Hamiltonian operator on a bounded interval

Consider the following Schroedinger equation on a bounded interval $[-a,a]\in \mathbb{R}$: \begin{equation} -\frac{d^2}{dx^2}\Psi(x)+V(x)\Psi(x)=0 \end{equation} with boundary condition \begin{...
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2 votes
1 answer
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Why are Amperes and moles both base units?

Current and "amount of substance" are base units The SI system treats both electric current and "amount of substance" as a quantity that is measured in "fundamental" or &...
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"All continuous time signals are analog but all analog signals are not continuous time"

I heard the above and pondered. The Wikipedia's definition for "analog signal" goes as follows "An analog signal is any continuous signal for which the time-varying feature of the ...
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Discreteness in quantum fields

I’ve heard a lot about discreteness and energy levels and things in the various books I’ve read on the subject, however I’m a little hazy as to how (if at all) this applies to quantum fields. Because ...
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1 answer
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How to prove that the fields' contribution to the action in Feynman's Path Integral are quantized?

The Lagrangian density in the path integral contains spinor, vector and number fields. However, their combinations in the action are scalars such as $\bar \psi \psi$, just numbers. Let's say I have an ...
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1 answer
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Is space build of smaller space-particles?

In atomic physics one of the most decisive proves that the objects are build of atoms is that they can be deformed and twisted. So is it not logical to believe that space itself is also build of ...
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Dirac delta identity, and intuition on normalization

I'm working through Quantum Field Theory for the Gifted Amateur by Lancaster and Blundell, and in Chapter 3 one of the problems is written like this: For boson operators satisfying $[\hat{a}_{\mathbf{...
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1 vote
1 answer
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Aren't we crossing infinity? [duplicate]

Couldn't there be infinitely small time units? When a second passes, aren't we passing infinite units of time? When we walk across a room, aren't we passing an infinite amount of small length units? ...
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1 answer
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Solving the 1d Schroedinger Equation numerically. How to get complex phases?

There is a nice method that lets you solve the Schroedinger Equation in 1d numerically, by discretizing space. Tranforming the Eigenfunction problem into an eigenvector problem with a finite-...
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3 votes
1 answer
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Confusion about $U(1)$ representations and charge quantisation in the context of gauge theory

In a gauge theory, the fields transform under representations of the gauge group. When studying a special unitary group $SU(n)$, I've usually thought of the elements of a representation as being the ...
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2 votes
0 answers
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Franck-Hertz experiment

In the Franck-Hertz experiment why are the peaks much sharper than the troughs? Also our data analysis suggested that the distance between the peaks is smaller (nearer to $4.9 \ $ eV ) than the ...
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Why the thermal radiation spectrum is continuous?

Why do photons within one body have different energies in a thermal radiation spectrum? Does it have to do with different modes of vibrations or phonons (for solid states)? In other words, is the ...
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2 answers
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Discrete Fourier transform intuition

I'm given a signal $$x(t)=\cos(200\pi t)$$ which is sampled at $t=n/400$ instance, for $n=0,1,2,..,7$ I've to comment on $X$, the 8 point discrete Fourier transform. Just multiplying by the DFT matrix ...
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1 answer
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Conservation of charge and quantisation of charge

How does the idea of conservation of charge relate to the quantisation of charge.
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1 vote
1 answer
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Quantization of the Berry Phase

Let's consider the Aharanov-Bohm effect. Following Girvin & Yang, an infinitely long, very thin flux tube running along the $\hat z$ axis is surrounded by a strong potential barrier preventing ...
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What are some references on discrete symmetries (CMT)

I'm a condensed matter theorist, and find that others in the field are very literate in consequences of breaking discrete symmetries. For example, there are a number of statements which often float ...
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1 answer
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Apart from quantum mechanical systems, how you will accept that energies are quantized? [duplicate]

Why energies are quantized at quantum scale? Apart from quantum mechanical calculations, how you will accept that energies are quantized?
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2 answers
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Is anything truly continuous? [closed]

Is any 'continuous' thing (fluids, light, time, etc...) truly continuous? Or is it really batch but at just such a high frequency that it appears to us as continuous? I.e. it appears to me that the ...
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Can an electron jump to a higher orbit with an energy that is only a little less than the theoretical requirment? [duplicate]

I understand that electrons can possess only discrete amounts of energy so if an electron in an atom has to jump from a lower orbit to a higher orbit it will require a discrete amount of energy to the ...
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3 answers
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Planck's quantum theory

Recently came across Planck's theory, $E = h\nu$. It means that at any frequency, there is given energy. But I also saw that, $E$ can be $0, h\nu, 2h\nu, 3h\nu,...$. How is it possible that energy can ...
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2 answers
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Is using traditional continuous calculus appropriate to study discrete Nature events such as quantum physics? [duplicate]

I was wondering why traditional calculus is used for studying quantum physics considering that there seems to be no continuum at quantum scale but discrete. For example, differential equations ...
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6 votes
2 answers
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Could wavefunction values be quantized?

According to standard quantum mechanics, Hilbert space is defined over the complex numbers, and amplitudes in a superposition can take on values with arbitrarily small magnitude. This probably does ...
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1 answer
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Asymmetric potential well and discrete energy levels

Let us consider an asymmetric potential, which is piecewise defined as $V_1$ for $x<0$, $0$ when $0<x<a$ and $V_2$ for $x>a$, together with the condition $V_1 > V_2 >0$. In the first ...
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0 votes
1 answer
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Do electromagnetic fields propagate continuously? [duplicate]

Having learned about plancks constant it is easy to mentally assign a grid-like structure to reality, almost starting to think of it as being pixellated in a way. This raises the question in me though ...
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Discrete quantities and calculus

Why we can apply calculus in cases where discrete quantities take place? Suppose we have a box that has two partitions, namely A and B (look at the figure below). Suppose we know the rate that ...
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