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.
647 questions
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Why do we consider time or motion continuous when our mathematics does not allow a continuous transition between real numbers? [closed]
Why is time or movement considered continuous when our mathematics does not allow a continuous transition between real numbers? For any two distinct real numbers $x$ and $y$ there is always a nonzero ...
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Classical vs. Quantum Oscillators
In introductory quantum mechanics, we learn that the energy levels of a quantum harmonic oscillator are discrete and given by the formula:
$$E_n = \hbar \omega \left(n + \frac{1}{2}\right).$$
However, ...
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Consensus(?) on whether space and time are really continuous (vs. discrete) [duplicate]
In current theories of physics, space and time are normally described as a continuum (like $\mathbb{R}^{4}$ or some other continuous manifold). Taken literally, this implies that there's no such thing ...
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How does time-independent Schrödinger equation imply the quantization of energy? [duplicate]
In Sakurai (3rd edition, p. 93), it is stated that the solution of the time-independent Schrödinger equation:
$$-\frac{p^2}{2m}\frac{d^2}{dx'^2}\psi_E(x')+V(x)\psi_E(x')=E\psi_E(x')\tag{1}$$
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Quantization of electromagnetic fields in vacuum
In Einstein's 1905 paper On a Heuristic Point of View Concerning the Production and Transformation of Light, he wrote:
"According to the assumption considered here, when a light ray spreads out ...
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Continuous volumetric heat source in finite difference heat equation [closed]
I'm currently working on a problem, trying to discretize a body with a continuous variable volumetric heat source ($\dot{q}(x, y, z)$, in $W/m^3$). I am running into an issue I feel like should be ...
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How to define an effective light cone or null direction from discrete arrival times on a lattice?
In several discrete or lattice-based approaches to spacetime (causal sets, Regge-like discretizations, lattice field theory, numerical GR, fast-marching/eikonal methods), one often works with a ...
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When can discrete curvature on a weighted graph reproduce an Einstein–Hilbert–type action in the continuum limit? [closed]
In several discrete-geometry approaches — such as Regge calculus, causal sets, and graph-based Ricci curvature — local curvature is defined combinatorially rather than through differential geometry.
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What is quantized/discrete in quantum mechanics? [duplicate]
When one quantizes a classical theory, one usually turns variables into operators and tries to find a canonical commutator relation that in some limit ($\hbar \rightarrow 0$) recovers the classical ...
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Problem with discrete time into spacetime models [duplicate]
Is this the essential problem of discrete time: suppose you decide that time is discrete, e.g. it only comes in integer "ticks". So an observer at rest says that event happened at times $𝑡=...
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Max speed in discrete space
Say that light moves N pixels/sec - does it imply that max speed for matter is <= (N-1) pixels/sec?
Does it imply and light will always outrun Rindler observer (constant acceleration in flat space) ...
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Trapped particle implies quantized energy levels? [duplicate]
I learned somewhere offhandedly that if classically, a particle would be trapped (have bounded position), then that implies the quantum counterpart would have discrete energy eigenvalues.
Obviously ...
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When can we apply quantization of angular momentum?
I am in high school and our teacher, while explaining the definition of orbits told us that according to Bohr model, electrons can exist only in the orbits where angular momentum of electron is ...
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2
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Can light emit all wavelengths, or only allowed energy levels?
Galaxies moving away emit redshifted light. If the speed of the moving away increases linearly, does the wavelength of the light also increase linearly, or discretely?
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Continuous and discrete energy
Isn't the phrase ‘energy cannot take any value’ misleading when describing quantized energy?”
I'm currently trying to understand the concept of quantized energy in quantum physics, and I’ve come ...
