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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How do we know the geometry of our physical world is made from real numbers and not rational numbers? [duplicate]
If I draw a line on a paper from point a to point b, how do we know that each point on the line exists in the real space, and not the rational space? How do we know if I randomly draw a dot, it won't ...
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What happens to left-over energy in atomic excitations?
The question relates to quantization of energy.
As we know, to make an electron jump to a higher energy level, a discrete amount of energy must be given to it. If the energy provided is less than the ...
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How can energy be discrete when momentum and position are not?
In quantum mechanics, it's said that the total energy of a system can only take certain discrete values. That is, the set of all possible energies of a system can be indexed by the natural numbers and ...
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Is it correct to say that a particle in the box can only acquire discrete velocities?
My thermodynamics lecture script says the following:
Translational Energy Levels
In addition to electronic energy, atoms have translational energy.
To find allowed translational energies we solve Ψ ...
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Continuity with respect to initial conditions
Buridan's Ass is a paradox that I am gradually, very grudgingly, beginning to accept as not-as-silly-as-it-seems. See the wiki article and this paper by Leslie Lamport. Quote: "Buridan’s ...
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An elementary question about an integration formula (nomenclature probably archaic)
so I am working on this research paper: https://docdro.id/sZsZiYL
Basically, the authors use a so-called Yee grid in order to discretize Maxwell's equations for computational purposes. In the paper, ...
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All periodic phenomena should have quantized energy levels?
I was watching a Lecture by Douglas Hofstadter on "Albert Einstein on Light; Light on Albert Einstein". And there was a slide which said that Einstein had idea that
All periodic phenomena ...
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How to understand why physics formulas are continuous while in microscope everything is discrete?
When I see physics formulas everything is perfect continuous everywhere, like momentum conserving Navier-Stokes equation, even like Schrödinger equation. But in atom scale everything is not continuous,...
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If spacetime is discrete, would we observe continuous models to show non-rounding and non-truncation errors?
Typically, the ground truth is taken to be the continuous model. Numerical simulations are taken to be the approximation. These simulations deviate from the continuous model due to both a constant ...
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Noether's Theorem application [duplicate]
So I know that Noether's theorem has a symmetry that corresponds to a conservation law.
I was wondering what quantity is conserved in charge conjugation symmetry.
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Asking about a clarification of a rather strange notation of a Yee Grid used for discretizing Maxwell's Equations
The thesis I am following requires me to discuss a rather strange formulation of a Yee grid used to discretize Maxwell's equations in order to solve them numerically mentioned in a research paper. The ...
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Why does electrons only acquire certain energy levels around an atom? [duplicate]
According to Bohr's hypothesis electrons can exist only at certain special distance from the nucleus only on certain particular orbits which is determined by Planck's constant, how does reach to this ...
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Why do bound electrons have quantized energy states but free electrons can occupy any possible energy? [duplicate]
Why do electrons have discrete energy states when they are bound to a nucleas and not when they are free for example in an electron beam. Why doesn't an electron beam have certain specified energies ...
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Quantization of a charge encoded in terms of cohomology
Could somebody untangle following statement I found here:
the integer cohomology groups correspond to the quantization of the electric charge.
I know from pure mathematical side the meaning of ...
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Is nature discretizable? [duplicate]
From mathematical perspective, can we describe all the realistic quantum mechanical phenomena at any given moment by functions alone, or is it correct that distributional behavior can also be observed ...
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Dirac delta in Fourier space for finite volume
In some class notes about cosmology I have found the following claim. The author starts by stating that the Dirac delta is given by:
$$\delta^{(D)}(\vec{x}+\vec{x}')=\int\dfrac{d^3q}{(2\pi)^3}e^{i(\...
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Discrete-time-dependent Hamiltonian from sequence of unitaries
Consider a system evolving in discrete time with the time evolution given by a some unitary operator $\hat{U}(t)$ that advances the system by one time step, i.e. $$\psi(t+1) = \hat{U}(t)\psi(t).$$ The ...
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What is the conservation law associated with isotropy of time? [duplicate]
I am reading Landau and Lifshitz’s Mechanics, where they explain how the conservation of momentum and angular momentum follow from the homogeneity and isotropy of space, respectively. They also show ...
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Peskin and Schroeder path integral discretization
I'm reading section 9.2 of Peskin and Schroeder, specifically where they begin the explicit computation of the two point correlation function for a free scalar field using the path integral (p.285). ...
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Why are the eigenvalues of position and momentum never quantized? [duplicate]
In ordinary non-relativistic quantum mechanics, the eigenvalues of the Hamiltonian, which represent the allowed energies of the system, are often quantized. For example, the energy levels of harmonic ...
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Rigorous proof that energy level of helium is discretized [duplicate]
For the hydrogen atom, a simple separation of variables give the energy eigenvalue of the Schrodinger operator for one electron in a spherical potential. It is well known that there are no such ...
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Is there an explanation for why electric charge, or hypercharge, are rational multiples of each other? [duplicate]
Electromagnetic charges are obviously quantized - I suppose the lowest charge being the $d$ charge of $e/3$. Every other charged particle has a multiple of that charge (actually all stable free ...
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Eigenstates for quantized oscillator [closed]
Hi I am new to solid state physics and am reviewing a prior knowledge section and would like some clarification. The following appeared in the course notes:
From my understanding, Eigenstates are ...
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Average of calculated quantity of discrete data
Let's say I have two discrete series of a physical quantity, current I and voltage V taken at the same time interval in a DC circuit. Now, I want to estimate the average power P over N measurements, ...
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Is entropy in the third law of thermodynamics a continuous quantity?
In the third law of thermodynamics, entropy goes to zero or to a constant value at vanishing absolute temperature. The change of entropy also goes to zero.
The third law is valid in the thermodynamic ...
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Is a continuum of bound states possible in a finite system Hamiltonian with a Coulomb potential?
I am wondering if it is possible to have a continuum of bound states in a finite system, for example a molecular system with a fixed number of nuclei and electrons. As a chemist, I'm used to ...
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Confusion in calculating entropy from continuous molecule abundances in discrete voxels
I am writing a simulation that includes chemical reactions and I think I am getting some things wrong with entropy and Gibb's free energy.
I was calculating the overall entropy of my system at a ...
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Quantum state in continuous basis [duplicate]
If I have an arbitrary state $|\psi\rangle$ and want to represent it in a continuous basis, for example the position basis in $x$-direction, I will get
$$|\psi\rangle = \int dx\, \langle x|\psi\rangle|...
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Are there any physical phenomena (or any phenomena at all) that are independent of time?
I am writing a discrete event simulation engine. I am trying to figure out if there is anything that I cannot model. (As my system uses a time step as basic unit of change).
I can think of some ...
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The continuum limit of the path integral & differential operators
When deriving the path integral formulation at one reaches an expression of the form
$$
\intop \prod_n dx_n \prod_n dp_n e^{\frac{i}{\hbar } \Delta t \sum_{n} (p_{n+1} \frac{x_{n+1}-x_{n}}{\Delta t}-...
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Are dualities symmetries? If so what are their conserved charges?
The dualities described the theories under certain transformations to be equivalent, i.e. $T$-duality described the equivalence between theories with $R$ and $\frac{1}{R}$. However, this looked very ...
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Why is the $\vec k$ space in solid state physics discretized?
I can't find a satsifying explanaition for the fact that the components of the $\vec k$ vector only take discretized values $$k_i = 2\pi n_i/L_i \qquad i\in {x,y,z}$$ with $L_i$ being the periodicity ...
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Why discrete gauge fields must be flat?
I found in some papers, for example "Generalized Global Symmetries" and "Generalized Symmetries in
Condensed Matter", that the gauge field of a discrete symmetry must be flat, i.e. ...
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Convergence of Feynman path integral in QFT
In Greiner field quantization book, when discussing the Feynman path integral approach, the book tries to calculate the path integral
$$\tag{12.35} \int \mathcal{D}\phi \exp\bigg[\frac{i}{\hbar}\int d^...
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Why is Wien's displacement law not discrete? [duplicate]
We are taught that the electrons emit electromagnetic waves/photons when transitioning from one quantum level to another in a discrete manner. This is what causes the spectral line of specific ...
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How do electrons move in 0D crystals?
It is said that quantum dots are artificial atoms that have discrete levels of energies, and has discrete energies in the density of states. What does it mean by the density of states in this case? ...
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How many colours is light made up of?
How many colours is light made up of?
Should it be infinite because of colours like light-blue , fluoroscent-blue , cyan ,dark green , sap green , etc.?
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Why, in low energy situations like atomic physics, are massive particles found to be in integer number states?
In quantum field theory electrons are conceptualized as quantized excitations of the quantum electron field. Generically the electron field can be in a superposition of number states. This is related ...
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Continuum mechanics from a simple spring model?
I was trying to see if a simple spring model would reproduce continuum mechanics. My reasoning was that (at least in metals), the atoms form a lattice held together by forces that can be well ...
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Construction of the Klein-Gordon field theory - what is missing?
Many references I know on QFT start the discussion of the Klein-Gordon field theory with some discussion about harmonic oscillators. One such reference is Folland's Quantum Field Theory book. The idea ...
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Confusion About Energy Bands
I read about energy bands in a physics textbook, and I couldn’t understand one thing about them. The book defines an energy band as continuous energy levels of electrons that are so plentiful that ...
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$\varphi^4$ propagator of the complete theory with cut-off in position: can I define things like that?
I am interested in a theory that reduces to a Euclidean $\varphi^4$ one in a specific limit. I want to calculate the full propagator of the theory, which means not using the perturbative expansion. I ...
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Differential charge existing
We define current by $I=\frac{\mathrm{d}q}{\mathrm{d}t}$. Here, $\mathrm{d}q$ is the infinitesimal element of charge. But again,we know that charge is quantised meaning there is a finite value to the ...
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Why are the energies of bound states quantized? [duplicate]
What mathematical condition can be invoked to justify quantization?
I would say that it is the boundary conditions by which the quantization is justified. Because thereby, only certain wave functions ...
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Any idea how to apply the Euler forward method to the Cart Inverted Pendulum (CIP)?
Well basically, as the title suggests. Considering the inverted pendulum
After going through the derivation of equations of movement I got the following two equations (thankfully I reached the same ...
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When does an operator in Quantum Mechanics have a discrete spectrum? [duplicate]
Say one has a classical Hamiltonian system with generalised coordinates $q$ and conjugate momenta $p$. After canonical quantization, promoting them to operators $\hat{q}, \hat{p}$, how can one ...
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Can the path derivative be defined with a non-constant measure?
I am trying to make sense of the following functional integral in the continuous limit:
$$
G({\bf x},{\bf y})=\lim_{N \to \infty}\int \prod_{k=1}^{N-1} d^2 {\bf z}_k \prod_{n=1}^N dp_n \exp\Bigg\{i\...
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How is the path-integral over a spatially finite region calculated?
The partition function for a system in the path-integral formalism is given by
\begin{equation}
\mathcal{Z}=\int\mathcal{D}\psi\mathcal{D}\psi^{\dagger}{e^{\int_0^{\beta}d\tau\int_Vd^3x\mathcal{...
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Is there a quantum gravity theory where ''space is discrete''?
I have been reading up on some approaches to quantum gravity apart from string theory. The popular conception of loop quantum gravity is that it says that space is actually physically discrete at ...
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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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