What is Spectrum: Definition and 764 Discussions

A spectrum (plural spectra or spectrums) is a condition that is not limited to a specific set of values but can vary, without steps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors in visible light after passing through a prism. As scientific understanding of light advanced, it came to apply to the entire electromagnetic spectrum. It thereby became a mapping of a range of magnitudes (wavelengths) to a range of qualities, which are the perceived "colors of the rainbow" and other properties which correspond to wavelengths that lie outside of the visible light spectrum.
Spectrum has since been applied by analogy to topics outside optics. Thus, one might talk about the "spectrum of political opinion", or the "spectrum of activity" of a drug, or the "autism spectrum". In these uses, values within a spectrum may not be associated with precisely quantifiable numbers or definitions. Such uses imply a broad range of conditions or behaviors grouped together and studied under a single title for ease of discussion. Nonscientific uses of the term spectrum are sometimes misleading. For instance, a single left–right spectrum of political opinion does not capture the full range of people's political beliefs. Political scientists use a variety of biaxial and multiaxial systems to more accurately characterize political opinion.
In most modern usages of spectrum there is a unifying theme between the extremes at either end. This was not always true in older usage.

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  1. thaiqi

    Quantum Which books are good for learning spectrum computation?

    Hello everyone. I 'd like to learn how to calculate the spectrum for elements. Which books are recommended?
  2. Q

    A Invariance of discrete Spectrum with respect a Darboux transformation

    According to this this the Darboux transformation preserves the discrete spectrum of the Haniltonian in quantum mechanics. Is there a proof for this? My best guess is that it has to do with the fact that $$Q^{\pm}$$ are ladder operators but I'm not sure.
  3. M

    MHB Exploring the Spectrum of φ - Eigenspace in Finite Fields

    Hey! 😊 For a prime $p$ we define $\mathbb{F}_p:=\mathbb{Z}/p\mathbb{Z}$. Let $\mathbb{K}\in \{\mathbb{F}_2, \mathbb{F}_3, \mathbb{F}_5\}$ and let \begin{equation*}a=\begin{pmatrix}0 & 1 & 0 & 5 \\ 1 & 0 & 2 & 3 \\ 0 & 0 & 0 & -1 \\ 0 & 0 & 1 & 0\end{pmatrix}\in M_4(\mathbb{K})\end{equation*}...
  4. W

    B Nearly Scale Invariant Power Spectrum in inflation

    I recall hearing once a very intuitive explanation as to why inflation is thought to lead to a nearly scale invariant power spectrum but i can't recall it. Can anyone offer an explanation that might help me? Why is it nearly scale invariant and not perfectly scale invariant? many thanks
  5. G

    A Bremsstrahlung single photon or spectrum

    Non-relativistic Bremsstrahlung is discussed classically in Rybicki “Radiative Processes in Astrophysics” where Larmor’s formula is used to find the power radiated in a collision between an electron and a Coulomb field. The Fourier transform of the pulse allows for a description of the pulse in...
  6. R

    Doppler effect and how it affects the light spectrum

    Looking for a beginners explanation to the following question: How is Doppler effect separated from the original spectrum of light emanating from a moving body (in astronomy or other physics branches)? If the question does not make sense, here is the reasoning to ask it: If a certain color is...
  7. B

    Angular width of first-order visible spectrum

    This is a diffraction grating problem I have been given that I am trying to answer Made a attempt at it and just wanted to see if I done this correctly or not? I get an angular width of 0.71 degrees which is very small Any help is much appreciated! Thanks
  8. S

    Delayed neutron energy spectrum

    First: what precisely is the shape of delayed neutron energy spectrum for each single emitter, generally? Second: what are the delayed neutron energy parameters for the common isotopes producing them? The attested list seems to be: Br-87 55,65 s 2,52 % Cs-141 24,8 s 0,035 % I-137 24,13 s 7,14 %...
  9. Sofi25l

    Why is the Hydrogen Spectrum Ambiguous?

    I was asked in a test this question: Electron in hydrogen falls from level 4 , how many lines we will see on the ejection spectrum? I hope I translated it well. I see a lot of question about those lines but can’t find information about it. Can anyone explain it to me?
  10. anorlunda

    Night On Earth: Uncovering the Infrared Spectrum of Animals

    I've been watching an interesting nature program on Netflix called Night On Earth. The film was all taken at night using low light and infrared cameras. I was surprised how many animals and insects see well at night. It makes me curious. Do we know how much of the infrared spectrum...
  11. carter7gindenv

    I Why is the black body spectrum bell shaped if it's absorptance is equal to 1?

    This bother me too much. A black body is said to absorb every incoming radiation. Looking at absorptance we have : A=Φabs/Φreceived So if a Black body absorbs everything we have A=1 Φ is a flux meaning object/time. This means that whatever the wavelength a black body will absorb the maximal...
  12. Kaguro

    I Spectrum of a function vs of a matrix

    The Fourier transform of a function is called its spectrum. The set of eigenvalues of a matrix is also called a spectrum. Why the same name? Is there some hidden connection between these two?
  13. arcTomato

    Comp Sci Power spectrum when the wave number is not an integer

    Hi all. I made a program of DFT, so I made the power spectrum of a sin wave. This is the sin wave I used. All data number ##N=100## and the frequency of sine wave is 4.5Hz. And the power spectrum is this. The wave number is not integer so the spectrum has the side lobe. But I think this is...
  14. arcTomato

    The power spectrum of Poisson noise

    Dear all. I have made the power spectrum of Poisson noise(expected value ##λ=2##), and it becomes like this I think this is not good. I don't know why the power is so high when Random variable(x axis) is 0. I tried another expected value version ,but the result didn't change. so I would like to...
  15. B

    Hydrogen emission spectrum calculation

    I've first method I tried was using f = v/λ to find the frequency, then E = hf to find the energy and then using E = (-13.6eV/n^2) - (-13.6eV/n^2) to rearrange and solve for the unknown n. However I got 5, the same as the original entry level. I also tried using 1/λ = R(1/4 - 1/n^2) to solve...
  16. arcTomato

    I I would like to know the calculation process of this power spectrum

    Summary: Derive the formula of power spectrum from Discrete Fourier Transform. Hi all I don't know where should I post this, so if I am wrong, I apologize.(But this is almost math problem so ) I would like to know the calculation process when derive Eq(6.3) in this paper. Eq 2.4a is...
  17. D

    A In the power spectrum, why is the peak frequency at the first harmonic

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  18. S

    A Calculating the Gravitational wave spectrum with Inflation as a source

    I am interested in knowing how to calculate the gravitational wave (GW) spectrum with inflation as a source, I have some background in inflation but I am not so familiar about calculating the GW spectrum. I am reading a paper (https://arxiv.org/abs/0804.3249) about it, however, a big part of it...
  19. arcTomato

    Engineering The power spectrum of a sine wave (C language)

    Hi I would like to Derive the power spectrum of sinusoid.I tried like this. But It doesn't work. <Moderator: CODE tags added> #include <stdio.h> #include <math.h> #define pi 3.1415926535 FILE *in_file, *out_file; int main() { dft(); } int dft(int argc, char *argv[]) { char...
  20. QuasarBoy543298

    I Deduce if the spectrum is discrete/continuous from the potential

    I have one-dimensional problem with a one-dimensional potential I want to know the energy domains that will result in discrete energy levels and the energy domains that will result in continuous energy levels In my lecture, my professor gave the example of v(r) = 1/r (r>0) (hydrogen atom...
  21. C

    A Spin change of Fermions and quantum energy spectrum

    Okay i was reading abrikosov's book and he said since in QM spin only changes by integer values boson excitiation happens one at a time and fermion ALWAYS appears or disappears in pairs. but isn't change from a spin up to spin down 1/2 to -1/2? or i had the wrong convention which |1/2| shouldve...
  22. Sunny Singh

    B Normalizability of continuous and discrete spectrum

    I was reading introduction to quantum mechanics by DJ Griffiths and while discussing the formalism of quantum mechanics, he says that if for a hermitian operator, the eigenvalues are continuous, the eigenfunctions are non-normalizable whereas if the eigenvalues are discrete, then they can be...
  23. SebastianRM

    I How Does Kirchoff's Law Relate to Spectrum Intensity and Wavelength?

    What is the author meaning by that, I literally just read in section 5.1, that the depending on the energy loss of the electrons that make up the substance, this energy will be released as photons. Since this is particular for each atom, it explained how we can tell which element is wich. So if...
  24. S

    Absorption Spectrum Practice problem

    Summary: The experimentally measured absorption spectrum of 1,3-pentadiene molecule exhibits a peak absorption (light absorption) around 224 nm corresponding to an electronic transition. Estimate the length of the molecule. I thought of using lambert law A = c*l*e but we have none. how do I...
  25. Meryka

    A What does the concave multifractal spectrum shape physically mean?

    I investigate the damage to the metal surface with box-counting method and some surface images give a convex multifractal spectrum f for a result - which is also widespread in the literature, but some other surface images form a concave multifractal spectrum. Not much information is available on...
  26. L

    Have you ever heard of the term "magnetic spectrum"

    Hello to all. This is my first post. I hope here is the right place to post. In a Greek secondary school book I found the term "magnetic spectrum" as the definition of the picture one get when we visualise the magnetic field. There is even a Greek Wikipedia page that I believe it comes from the...
  27. XLAYZ

    A Interpretation of Bi-207 decay spectrum

    I measured the decay spectrum of Bi-207 as a beta source with scintillation detector and now I am trying to interpret the information given by the spectrum. As far as I know, the Bi-207 nuclei decay to the excited states of Pb-207 primarily via EC and a small beta+ branch, emitting beta...
  28. neilparker62

    I Measuring the Helium Spectrum: Friederich Paschen 1916

    Re page 14 of following reference: https://zenodo.org/record/1447321#.XSyx3z9LjIU If I understand correctly this page is showing a set of measurements for the fine structure of singly ionized Helium at +- 4686 Angstrom. Can we figure out from this which specific transitions are being measured...
  29. B

    Looking for Freeware to Generate X-Ray Spectra? Check Out These Options!

    Hi there, Was just wondering if anyone knew of any good freeware for generating X-ray spectra from a standard Tungsten anode that you might see in medical radiography? Would be good if it could export data as well, but yeah and just wanting something that can potentially generate the spectra...
  30. S

    How bad will the sale of the spectrum down to 24.25 GHz be for weather radar?

    I was reading this, and got concerned: https://slate.com/technology/2019/05/spectrum-auction-bandwidth-weather-forecasting-fcc-noaa.html
  31. T

    I High resolution visible spectrum

    I'm trying to find a high resolution image that shows the visible electromagnetic spectrum with a fine graded scale. It should be detailed enough to pinpoint which exact colour corresponds to a particulate wavelength (integer in nanometer) of light. I find a lot of images through searches but no...
  32. J

    A How to obtain the spectrum for a given atom or simple molecule?

    The Bohr atom gave the answer to the spectrum of the hydrogen atom. But the spectra of stars contains many absorption (and sometimes emission) lines, corresponding to most atoms (up to iron, I believe). And atmospheric absorption is also due to absorption of some molecules, such as water...
  33. L

    B What region in NMR spectrum should I choose for integration?

    Hi all, I have nuclear magnetic resonance spectrum. The vertical axis is intensity, and the horizontal axis is index. I need to find integral under the peak. But I am not sure, what region should I choose for integration - region 1 or region 2? Please find attached the spectrum.
  34. M

    A Understanding the Spectrum of a Linear Operator

    Hi PF! What is meant by the spectrum of a linear operator ##A##? I read somewhere that if ##0## belongs in the spectrum, then ##A## is not invertible. Can anyone finesse this for me? I read the wikipedia page, but this was tough for me to understand. Perhaps illustrating with a simple example...
  35. koulbichok

    A Abundance and mass spectrum of PBH

    Hello. I'm trying to study primordial black holes for my work, but I still can't understand what are abundance and mass spectrum? Could you explain? Thanks in advance.
  36. Clara Chung

    Question about atomic spectrum

    I drew a picture of the information in the problem (not sure if it is right), the red lines are the given values and green line can be calculated using the formula given. I don't know how to find the defects because the energy from 100d to 100g is missing...
  37. N

    Overtone Spectrum Analysis Software

    I'm currently testing the overtone spectrum of several instruments. I haven't been able to find a freeware program that's well suited to my needs. In particular, I would like to be able to pause the playback of each overtone spectrum at specific intervals in order to compare the instruments...
  38. Q

    Network analyzer vs Spectrum analyzer

    I'm currently studying the network analyzer(NA) and spectrum analyzer(SA), and one thing makes me wonder; Would it be possible to 'mimick' a NA with a SA and a signal generator(SG)? Ofcourse some phase calculations may also be required, but from my naive understanding, if a NA sends various...
  39. jgarrel

    Quantum Field Theory-Mass spectrum of Lagrangian

    Homework Statement We are given the Lagrangian density: $$ \mathcal{L}=\partial^\mu \phi ^* \partial_\mu \phi - m\phi^* \phi +\sum_{\alpha =1} ^2 ( \overline{\psi}^\alpha (i\gamma^\mu \partial_\mu -m)\psi^\alpha -g\overline{\psi}^\alpha\psi^\alpha \phi^* \phi) $$ , where ##\phi## is a complex...
  40. A

    A Influence on Neutron spectrum due to energy loss of beam

    Suppose some protons are impacted on a Lithium target to produce neutrons with energies close to the proton energy. If one considers Energy-loss due to proton-target collision (ionization of the target atoms), will this kind of energy loss influence neutron energy spectrum? I am asked by my...
  41. R

    A Nonlinear static polarization and impurity spectrum

    As is known, when calculating localized states in a crystal it is roughly considered that the point charge is “immersed” on medium with static dielectric constant ε. However, a simple estimate, for example, shows that an impurity atom with charge modulo equal to the electron charge creates at...
  42. N

    I Understanding what the complex cosine spectrum is showing

    The complex exponential form of cosine cos(k omega t) = 1/2 * e^(i k omega t) + 1/2 * e^(-i k omega t) The trigonometric spectrum of cos(k omega t) is single amplitude of the cosine function at a single frequency of k on the real axis which is using the basis function of cosine, right? The...
  43. X

    I Solar Spectrum: Continuous & Absorption Confusion

    Ok, I'm a bit confused with the spectrum of the Sun. Is the spectrum of the Sun continuous or absorption? Better yet, is it both? Or am I totally confusing myself? I understand that the source itself is continuous but it is partially absorbed (wrong phrasing?) as it passes through the outer...
  44. R

    I Spectrum classification and dimension reduction

    I am trying to distinguish two different plant species based on their chemical signature using statistical signal classification. This is what the average curves of two species look like with their standard deviation bounds: These spectra are made up of ~1400 points. So it was suggested to...
  45. T

    How is the horizon length related to the power law spectrum

    Homework Statement For a power spectrum density fluctuations ##P(k) \propto k^n##, I need to find the scaling (with respect to ##a##) of the horizon wavenumber ##\frac{2\pi}{\chi_H}## in a matter dominated universe in terms of ##n##. ##\chi_H(a)## is the evolving particle horizon, in a flat...
  46. W

    Recoil Proton Momentum Spectrum in Neutron Decay

    I wish to draw the proton momentum spectrum by transforming the energy spectrum of recoil protons. I have calculated the energy spectrum using Nachtmann's spectrum: wp=g1[T]+a*g2[T] Where: g1[T]=(1 - x2/σ[T])2 * Sqrt[1 - σ[T]] * (4*(1 + x2/σ[T]) - (4/3*(σ[T] - x2)/σ[T])*(1 - σ[T])); g2[T]=(1 -...
  47. starstruck_

    Spectrum of hot gas uniformly mixed with dust

    hey! EDIT: I didn’t post this in homework help because there aren’t any computational questions, it’s just conceptual My assignment scenario consists of a star (blackbody) surrounded by an expanding shell of hot gas. I’m given its spectrum and it is a continuous emission spectrum. Emission...
  48. B

    B How Can a Hydrogen Atom Emit Multiple Colors Simultaneously?

    If the spectral line of Hydrogen contains four colors, I don’t understand how the electron can jump four times to four different energy levels in the same moment?
  49. Spinnor

    I ....Alternatives to Inflation in Primordial Power Spectrum

    Unique Fingerprints of Alternatives to Inflation in the Primordial Power Spectrum "Massive fields in the primordial universe function as standard clocks and imprint clock signals in the density perturbations that directly records the scale factor of the primordial universe as a function of...
  50. B

    How do you work out the wavelegth (Franck-Hertz experiment)?

    Homework Statement In a Franck-Hertz experiment carried out with potassium vapour, it is found that the current falls off rapidly at an applied voltage of 1.62V. Calculate the wavelength of the expected spectral line in the emission spectrum of potassium when this voltage is reached. Homework...
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