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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1D Infinite Square Box Discrete Energy levels but Continous Momenta?

In the 1d particle in the box the energy of the particle should be completely determined by the momentum of the particle that you observe correct? So how can you have discrete energy levels and a ...
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0answers
45 views

Wannier Functions as Discrete Basis

In solid state physics, using Bloch's theorem we know that the one-electron energy eigen-function can be written as $\psi_{\lambda,\vec{k}}(\vec{r})$ where $\lambda$ indexes eigenvalues of $\hat{H}$ ...
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1answer
72 views

Turning a finite difference equation into code (2d Schrodinger equation)

I am trying to convert the following finite difference equations into code (taken from the bottom of page 12 of this thesis by Maike Schulte Numerical Solution of the Schrodinger Equation on Unbounded ...
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1answer
70 views

Interpretation of $\vec{x}$ in QFT

I am still at an early stage of studying Quantum Field Theory (I am reading QFT In A Nutshell by A. Zee). In the book I'm reading, it starts from a discrete lattice of material "lumps" labeled by ...
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1answer
100 views

What measurement of time is so small that it qualifies as quantum?

Quantum mechanics (QM; also known as quantum physics, or quantum theory) is a branch of physics which deals with physical phenomena at nanoscopic scales where the action is on the order of the ...
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0answers
11 views

Is Sorkin's causal growth dynamics a Galois Connection

Sorkin is well known for his causal growth dynamics. I think it is a sensible question to ask if his growth dyanamics, which I think can be seen as a poset map (though his work is much more ...
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1answer
69 views

Are temperature increases discrete? [duplicate]

Are temperature increases ever discrete in nature, or is it a continuous variable? If a discrete case exists, is there any material that exhibits particularly strange behavior?
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4answers
2k views

Are voltages discrete when we zoom in enough?

Voltages are often thought of as continuous physical quantities. I was wondering whether by zooming in a lot, they are discrete. I feel like the answer to the above question is yes as voltages in the ...
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3answers
111 views

Is the energy of a photon continuous/discrete?

I was struggling today with this question: does a free photon have a continuous energy spectra? Free means in no context of any energy system (eg. an atom, em field). Although I'm asking myself if ...
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0answers
38 views

Planck time, time or time interval? [duplicate]

Planck time is really a weird topic, if we try to find out that is it time or time interval. It is the time taken by light to travel a Planck LENGTH so it must be time interval. But we also know that ...
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1answer
80 views

Why is it more convenient to consider space or time as a continuum?

I often find that phisicists and cosmologists make use of Planck's units. I have read propositions that sound like "...at the level of Planck's units many law of physics break down" ...
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1answer
102 views

Is there an absolute minimum scale to the universe? If so, why?

Based on my rather circumscribed understanding of modern physics, one of the key insights of quantum mechanics over previous scientific theories is the prediction that there exists an absolute limit ...
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4answers
173 views

I don't get band structure of solids

If the energy levels of bound electrons are discrete, why do band structures in solids arise?
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1answer
72 views

Justification of discrete spectrum for V(x) unbounded at $\pm \infty$ in Pauling and Wilson

In Pauling and Wilson, Introduction to Quantum Mechanics, they offer the following intuitive reason for the discrete spectrum of a potential which is unbounded at $\pm \infty$: This is ...
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3answers
90 views

Units of a discrete Fourier transform

Normally a Fourier transform (FT) of a function of one variable is defined as $$f_k=\int^\infty_{-\infty}f(x)\exp\left(-2\pi i k x\right) dx.$$ This means that $f_k$ gets the units of $f$ times the ...
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1answer
45 views

How is that the life of a virtual particle duo is shorter than Planck Time?

I have always thought that the time is discrete (jumping), not continuous and the shortest time is Planck Time. One reason for that was the information on ...
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1answer
61 views

How is quantization implied by quantum mechanical theories? [closed]

Can anyone please explain(both by mathematical equations and by intuition) how the Schrodinger equation and Heisenberg matrix mechanics imply discrete states of energy, momentum etc and lead to ...
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4answers
837 views

How can there be really any instantaneous velocity?

I have read about Zeno's arrow paradox that tells us there is no motion of the arrow at a particular instant of its flight. It can be inferred that there can be no velocity at any instant. Moreover we ...
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0answers
32 views

Review and mentions about time discretization

I would like to get basic knowledge in this topic of time discretization, at least basics. Because of I'm new in this field I don't know what is better way to start. Could anybody suggest any reviews ...
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1answer
114 views

Is temperature discrete

Because an object's temperature is inversely proportional to the wavelength of blackbody radiation which it emits, physicists have theorized the existence of Planck temperature at around $1.4×10^{32}$ ...
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1answer
91 views

Discretizing the Wave Equation in polar coordinates

I want to discretize the wave equation $$\frac{1}{c^2}\frac{\partial^2\psi\left(\vec{r},t\right)}{\partial t^2}=\triangle\psi\left(\vec{r},t\right)$$ in polar coordinates. I find the following ...
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0answers
34 views

Quantized spacetime structure? [duplicate]

Is quantized spacetime more like a chessboard or a matrix of lights? I have heard two analogies, the light bulb one appears to allow for movement whilst the chess piece one seems to violate zenos ...
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0answers
27 views

Is spectrum of Discrete-Time Fourier Transform (DTFT) periodic or not

I can't think of any better title. Here is the content that I got question http://cnx.org/content/m10247/2.31/ As it state the nature of DTFT's spectrum is periodic as it show in figure 1 However, ...
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3answers
356 views

Formalism to deal with discontinuous potentials in classical mechanics (hard wall, hard spheres)

It seems to me that Hamiltonian formalism does not suit well for problems involving instantaneous change of momentum, like particle collisions with hard wall or hard sphere gas model. At least I could ...
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0answers
37 views

How to get discretization coefficients of matrix $A$ in Finite Volume Method (FVM)? [closed]

First we have Discretization of the Transport Equation $$ \frac{\partial \rho \phi}{\partial t} + \nabla(\rho U \phi) - \nabla (\rho \Gamma_\phi \nabla \phi) = S_\phi (\phi) $$ In Finite Volume ...
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2answers
105 views

Infinitely many points of space-time?

Please can someone provided me with academic literature (Journals/Books, titles & links) which discuss the current view on space time i.e. that there is not Infinitely many points of space-time?
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1answer
115 views

Is it possible that the universe in its entirety is discrete rather than continuous? [duplicate]

Since electric charge is comprised of discrete units and and mass is formed by discrete units is it possible that space-time itself is discrete as well?
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0answers
35 views

Are continuous mathematical models of discrete physical phenomena messy because of a disconnect between “continuous” and “discontinuous”? [duplicate]

A copy of my question on Mathematics: Examples from statistical mechanics and continuum mechanics abound: a discrete phenomenon (e.g. kinetic energy of molecules) is "averaged" out over the ...
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2answers
165 views

What is the “discrete” analogue to “continuum” mechanics?

If I wanted to explore a discrete mathematics approach to continuum mechanics, what textbooks should I look into? I suppose a ready answer to the question might be: "computational continuum ...
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1answer
145 views

What arguments are in favour of an atomic structure to space-time?

The atomic theory as first theorised by Democritus has been successfully applied to matter and to energy (quanta). Space-time is still generally seen as a continuum. What arguments are there (if any) ...
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1answer
156 views

Theoretical reasons for charge quantization

I'm aware of Millikan's oil drop experiment and I've read that quarks have fractional eletric charge, but I was wondering if there's any theoretical argument that makes us believe charge is quantized. ...
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1answer
42 views

Charge or Charges on the oil droplets?

Due to my poor understanding of various paper and other material provided by google on Millikan's oil drop experiment I ask the following question here. As the drops were charged by either friction ...
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2answers
231 views

Oil drop experiment and quantization of charge

How to systematically show that the resulting charges in oil drop experiment are integers multiplied by $e$ in other word how to extract $e$ from the data?
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3answers
121 views

Discrete movement vs wave function collapse

I remember once, as a child, thinking that objects do not really "move," but that at a very small scale they would have to "disappear" and then "appear" again at their newly shifted position, just the ...
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1answer
204 views

If time isn't continuous, what is the best-known upper bound on the length of time intervals?

There have been several questions about whether time is continuous or not and it seems like the answer isn't currently known. I know quantum mechanics treats time as continuous and any mathematics ...
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4answers
305 views

When is energy discrete/quantized for a potential well?

Specifically, my question is: Should one expect energy quantization for a particle in the following potential well? More generally, how can one tell whether or not energy should be ...
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2answers
89 views

Discrete approximation of charge density

Given the electric potential $\Phi(r)$ and the Poisson's equation: $$ \nabla^2 \Phi(r) = - 4\pi \rho(r)$$ Consider the 2-dimensional case and let's say that I want to discretize this using a square ...
2
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3answers
152 views

Configuration space of particles in the box

The notion of entropy says that we can count microstates that correspond to macrostate. But, I do not understand how this can be done. Does it imply that the state space is discrete (finite or ...
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1answer
197 views

Can universal continuity be experimentally falsified?

It is an unresolved question whether the universe is discrete or continuous in its intricate quantum level structure. See for example: Is the universe finite and discrete? How could spacetime become ...
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0answers
86 views

Is everything in the universe discrete? [duplicate]

When beginning my education, I regarded nearly everything as continuous and analog in nature: Physical objects could have any mass on a continuous scale Light sources could emit any intensity of ...
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1answer
125 views

Explicit solutions to 2-d Dirac Equation

The 2-d Dirac equation without any constants is represented usually as $$i*dt (\phi) = D (\phi)$$ where $D = m\sigma_2-i\sigma_1dx-i\sigma_3dy$. Where can I find explicit closed form solutions to ...
4
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1answer
273 views

What fundamental reasons imply quantization?

In classical wave mechanics, quantization can occur simply from a finite potential well. In quantum mechanics, the quantization is obtained from the Schrödinger equation, which is, to my knowledge, a ...
2
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1answer
464 views

Planck time & length

Why is Planck time the shortest possible duration ever? It's defined as the duration needed by light to travel Planck's length, but surely, give me any number, I can give you a lower number than that? ...
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2answers
948 views

Continuous vs. Discrete Spectra in various materials

I read that the reason solids emit continuous spectra is that they don't have time to let their electrons decay-they are too close together. Given that electrons decay on the order of 100 nanoseconds ...
0
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1answer
188 views

Quantization of Electron Spin

Why is electron spin quantized? I've seen the derivation for the Hydrogen atom's energy levels, but my professor jumped to electrons having spin 1/2 or -1/2 as experimental. Why do electrons obey the ...
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4answers
554 views

Is the electromagnetic spectrum discrete?

I'm just starting to learn physics and I have a question (that is probably stupid.) I learned that energy levels that the bound electron can have are discrete. I also learned that when an electron ...
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2answers
416 views

The Quantization of Photon Energies

Despite Planck's constant being in $E=hf$, it would appear to me that energy is still not discrete, as frequency can be an fraction of a Hertz that one wants. How does this imply that electromagnetic ...
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4answers
1k views

Bounded and Unbounded (Scattering) States in Quantum Mechanics

I understand that bounded states in quantum mechanics imply that the total energy of the state, $E$, is less than the potential $V_0$ at + or - spatial infinity. Similarly, the scattering state ...
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0answers
101 views

Wave Particle duality because of discrete time?

If time is discrete, such as the Planck's length, would the transition from one frame of time to the next explain why it appears matter changes from a particle to a wave? During that infinitely small ...
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3answers
279 views

Computation theory and the simulation argument

Can physical states be treated as information (strings over some alphabet)? If (1) is true, isn't this a trivial conclusion that the universe can be simulated by a Turing machine or a cellular ...