What is Spectrum: Definition and 765 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. ergospherical

    I I'm slightly confused about the power spectrum of matter

    How do you get these scalings for the matter power spectrum?$$P_{\Delta}(k) \sim \begin{cases} k & \quad k < k_{\mathrm{eq}} \\ k^{-3} & \quad k >k_{\mathrm{eq}} \end{cases}$$(N.B. ##k_{\mathrm{eq}}## is the scale of modes that enter the horizon ##k \sim \mathcal{H}## at matter-radiation...
  2. Anisur Rahman

    How Can I Simulate a Narrow Spectrum X-Ray Beam Using MCNP?

    I don't know where is the problem. My supervisor couldn't provide me the actual specification of my X-ray tube. I was asked to simulate the X-ray narrow spectrum beam. I run that code, but it produces nothing. Can anyone help me?
  3. RobbyQ

    I Electromagnetic Absorption in the Ocean

    The recent rescue operation of a sub in the ocean made me wonder how difficult it is to communicate with underwater vessels. Is it that all parts of the EM spectrum gets absorbed at extreme depths that things like GPS is not possible. I wondered what wavelengths of the spectrum were absorbed...
  4. R

    Show that the minimum in alpha-decay spectrum is caused by interference of peak

    This problem set considers (beta-delayed) alpha decay of ##{}^{20}Na##. I'm currently stuck in the following exercise and was hoping some of you could help me in the right way. Thanks in advance! The problem is: c) The experimental spectrum of ##{}^{20}Na## can be found below. Apart from peaks...
  5. R

    A What does the TE CMB spectrum reveal?

    Does the polarization spectrum TE measured by the Planck and WMAP satellites show evidence for superhorizon fluctuations at low multipoles and are these evidence for pre-bigbang inflation?
  6. SherLOCKed

    I Maximizing S/N in Angular Power Spectrum Signals

    The signal-to-noise ratio for angular power spectrum signal Cl under theoretical noise Nl, where Cl and Nl are functions of multipole l, is given as (S/N)^2= \sum (2l+1) (Cl/Nl)^2To increase the S/N we bin the power spectrum signal, if bin width \Delta l, this in principle decreases Nl by a...
  7. Pushoam

    Spectral lines in the emission spectrum for an electron at n= 3

    Since there is only one excited electron, it could come from n=3 to n =1directly or n=3 to n =2 and then n=2 to =1. Hence, there could be one or two lines depending upon the path taken by electron. Is this right?
  8. armoredchestnut

    Hybrid/variable spectrum reactor

    Why have no Variable spectrum reactors been produced? A reactor that could start by burning natural U, like the CANDU or RBMK, and then transition to a fast spectrum seems to be ideal. Running nuclear fuel from raw material to nuclear ash all in one reactor seems to be the solution for people...
  9. Dave Gungan

    I How to interpret this new Keck spectrum picture of Jupiter?

    Last night, on Wednesday, November 9, the KPF team successfully captured a first light spectrum of Jupiter with the next-generation instrument This spectrometer picture of Jupiter has just been taken by the Keck, but I don't understand it. Wiki says Jupter is "89%±2.0% hydrogen" and "10%±2.0%...
  10. A

    A Spectrum of the Liouville Operator

    Context: Consider a classical system with Hamiltonian ##H##. The Liouville differential operator can be defined using the Poisson brackets as $$L=-i\left \{ ,H \right \}.$$ ##L## is Hermitian in the Hilbert space of square integrable wavefunctions over phase space. The spectrum of ##L## is easy...
  11. Conn_coord

    I The CMB has a thermal black body spectrum

    https://en.wikipedia.org/wiki/Wien's_displacement_law "Maxima differ according to parameterization ... Using the value 4 to solve the implicit equation yields the peak in the spectral radiance density function expressed in the parameter radiance per proportional bandwidth. (That is, the density...
  12. H

    I Partition function for continuous spectrum

    Let's say that we have a one-particle Hamiltonian that admits only a continuous spectrum of eigenvalues ##E(k)=\alpha k^2## parameterized by asymptotic momentum ##\mathbf{k}## (assuming the eigenfunctions become planewaves far from the origin), would the partition function then be $$Z=\int...
  13. stephen8686

    I Propagation of Angular Spectrum Code

    I'm making a MATLAB code to propagate a gaussian field in the angular spectrum regime (fresnel number >> 1). After Fourier transforming the field, you propagate it: $$U(k_x,k_y,z) = U(k_x,k_y,0)e^{ik_z z}$$ The thing that I am having trouble with is the propagation factor, I have looked at this...
  14. L

    A Photon-Phonon Cavity Spectrum

    I am considering the following Hamiltonian: $$H = -\Delta a^{\dagger}a + \omega_m b^{\dagger}b + g_0 * a^{\dagger}a (b + b^{\dagger})$$ which is the interaction picture optomechanical Hamiltonian for a cavity with movable end mirror. The mirror vibrations are quantized, leading to phonons that...
  15. D

    Landau Energy Spectrum in the non-relativistic limit

    At non-relativistic limit, m>>p so let p=0 At non-relativistic limit m>>w, So factorise out m^2 from the square root to get: m*sqrt(1+2w(n+1/2)/m) Taylor expansion identity for sqrt(1+x) for small x gives: E=m+w(n+1/2) but it should equal E=p^2/2m +w(n+1/2), so how does m transform into p^2/2m?
  16. D

    I Experimental demonstration of an absorption spectrum

    Hello, is there a convincing experiment to visualize absorption spectra? At disposal I have: - Halogen lamps - Lenses - Straight view prism - transmission grating - slit, iris, screen - Sodium vapor lamp and mercury vapor lamp Unfortunately, I do not have a sodium vapor cell or anything...
  17. C

    A Physical explanation of time-correlation function and spectrum

    From my reading of several quantum optics textbooks and spectroscopy texbooks, the emission and absorption spectrum of an atom or molecule are always given in terms of the time-correlation function, for example the emission spectrum of a two level atom is given by: $$...
  18. T

    Engineering Spectrum analysis of unbalanced rotating rotor

    Spectrum of acceleration vs frequency Results of balanced condition Results of unbalanced condition
  19. C

    A Absorption and emission spectrum in quantum optics

    The emission spectrum or resonance fluorescence for a quantum dot, atom or defect center are discussed in many quantum optics textbook, for example see "Quantum Optics" by Marlan O. Scully and M. Suhail Zubairy Chapter 10 , "Quantum Optics" by D. F. Walls and Gerard J. Milburn Chapter 10 and...
  20. dark_nebula

    Question regarding a decay spectrum graph

    I am not sure what is the description of Channel.
  21. Mr X

    B How does the hydrogen line spectrum work with only one orbit?

    Since hydrogen atom has only one orbit, how does the hydrogen line spectrum work? I saw somewhere, that infinite orbits(n) are possible, but wouldn't having too much energy end up causing the electron to break free from the nucleus and thus ending up as a free electron? So when exactly does...
  22. Sippi7299

    Chemistry Processing a "Raw Spectrum" - A Beginner's Attempt

    The first picture shows the "raw spectrum" before processing it and the second one is my attempt to process it. I was not sure about the solvent peak because it is expected to be a singulett at 7,26 ppm but I could not really identify a clear singulett so I dichtet to go with the peak that stood...
  23. Sippi7299

    Biotechnology Student from Germany Needs Help Analyzing NMR Spectrum

    hello, I'm form Germany and study biotechnology in my third semester and have to find an unknown substance by using an NMR spectrum. Unfortunately I have almost no experience in this field. Is here somebody who could help me analyze the spectrum? I would be very thankful
  24. ktmsud

    I Continuous Spectrum and Energy levels of Electrons (Energy Bands)

    My book says that emission spectra are produced when an electron in excited state jump from excited to lower energy states. It also states that solids and liquids produce continuous spectra and it depends upon temperature only (is this black body radiation?). I know, Electrons around a nucleus...
  25. W

    I Question about electromagnetic spectrum and solar cells

    Would it be possible to change all wavelenths to one frequency that would then be sent to a solar panel adapted for it, or once split could to be sent to cells that work in that range? In other words use all the light to produse electric power
  26. arcTomato

    I Is my calculation of the power spectrum correct?

    Hello PF. I am thinking about the power spectrum when observing X-rays. We are trying to obtain the power spectrum by applying a window function ##w(t)## to a light curve ##a(t)## and then Fourier transforming it. I have seen the following definition of power spectrum ##P(\omega)##. Suppose...
  27. arcTomato

    I The power spectrum of Poisson noise

    I thought that if we Fourier transformed the counts of the sum of the signal from the source and the Poisson noise, and obtained the power spectrum, we would get the following, ##P_{j}=P_{j, \text { signal }}+P_{j, \text { noise }}+\text { cross terms }## but I found the following description...
  28. muissi97

    Chemistry Emission Spectrum of an element

    The difference in energy between these two lines is that in the ultraviolet spectrum line, there is more energy because it has a shorter wavelength compared to the visible spectrum line as shown in figure 1.1 According to the Niels Bohr's model of the atom(figure 1.7) and figure 1.1, the least...
  29. F

    A LIF Spectrum: Understand 12 Branches & Subscripts

    I have a bit basic understanding of spectrum, but quite confused with LIF spectrum. It seems existing 12 main branches of Laser induced fluorescence, such P1, P2, Q1, Q2, P21, R21,and so on. I know there should be O P Q R S branches of the rotational transitions, but where these so many...
  30. F

    A Relation between Matter Power spectrum and Angular power spectrum

    From a previous post about the Relationship between the angular and 3D power spectra , I have got a demonstration making the link between the Angular power spectrum ##C_{\ell}## and the 3D Matter power spectrum ##P(k)## : 1) For example, I have the following demonstration, ## C_{\ell}\left(z...
  31. nomadreid

    I Confused about the spectrum of an observable

    This is a very elementary question, from the beginnings of quantum mechanics. For simplicity, I refer to a finite case with pure states. If I understand correctly, the spectrum of an observable is the collection of eigenvalues formed by the inner product of states and hence equal to...
  32. snypehype46

    I Mass spectrum of open bosonic strings

    I'm learning string theory from the book by Zwiebach and others. I'm trying to understand the quantisation of the open string and its mass spectrum. In light-cone gauge the mass-shell condition of an open string is given by: $$M^2 = 2(N - 1)/l_s^2$$ where ##N =...
  33. SJay16

    How would one estimate the rotation period of a star from its spectrum

    The figure is shown; the measurements were taken on two consecutive observing nights. The Ordinate is the flux normalized to continuum and the abscissa is the wavelength scale. You can see the "bumps" indicated by the arrows referring to some Starspot as the spot moves on the profile; assuming a...
  34. snypehype46

    Computing the spectrum of a Lagrangian in field theory

    I have the following lagrangian density: $$L = \bar{\psi}i \gamma^\mu \partial_\mu \psi - g\bar{\psi}(\sigma + i\gamma^5\pi)\psi + \frac{1}{2}(\partial_\mu \sigma)^2+ \frac{1}{2}(\partial_\mu \pi)^2 -V(\sigma^2 + \pi^2)$$ where $\pi$ and $\sigma$ are scalar fields. I have show that this...
  35. C

    I Optical spectrum analyzer related

    Can anyone explain why optical spectrum analyzer plots are in negative dB
  36. B

    What causes the peak in the thermal noise spectrum of an RLC circuit?

    Hello! Below is a figure of the thermal noise spectrum of an RLC circuit from a certain experiment. I am not sure I understand the shape. The spectrum is peaked around the resonant frequency. However, in thermal equilibrium, I would expect that the electrons to have random motions, so for a...
  37. F

    A Angular power spectrum dependence in redshift z and k

    Hi, I wanted to have a precision about a question that has been post on this relation between P(k) and C_l The author writes the ##C_\ell## like this : $$C_\ell(z,z') = \int_0^\infty dkk^2 j_\ell(kz)j_\ell(kz')P(k)$$ I don't undertstand the meaning of ##z## and ##z'## : these are not...
  38. A

    I How do I properly plot the solar spectrum and handle the flux of Arcturus?

    I'm trying to plot the solar spectrum (Wavelength versus Flux) from a table of values I'm given. I'm given 3 columns; Solar Flux Arcturus Flux Wavelength Plotting Solar Flux versus Wavelength gives me a graph (below) that is very difficult to resolve. There are 21,000 data points as well. If...
  39. M

    Signal Processing: DFT spectrum of sinusoid signals

    Hi, I was recently reading about the discrete Fourier transform and its application to a basic sinusoidal signal. If we know that it has an integer number of cycles in ## N ## samples (and thus no leakage), why would there be two peaks in the spectrum: one at ## m ## and another at ## N - m##...
  40. F

    Engineering Sketch the spectrum of the DSB-SC signal

    Here's my work: Could someone please confirm my answer?
  41. R

    I Explaining the Continuous Diffraction Spectrum of a Heated Solid

    This is the figure from the book. First of all, from what I know about diffraction, there is an interference pattern but not dispersion of the different colors. If what is happening here can be explained that would be great. Second, the book says the line spectra for different gasses are due to...
  42. F

    Is MCNP capable of scoring fission spectrum?

    Hi everybody, I am trying to score fission spectrum in MCNP for a kcode calculation. I would like to check at which energy neutrons produced by fission are generated. I have no idea how to perform since tallies are usually volume or material dependent and I just want to build a spectrum...
  43. small physicist

    Spectrum of laser light absorbed and re-emitted by a white object

    Hello, If I shine a red laser onto a white surface, I assume that: some of the red light will be nearly instantly reflected, some will be absorbed and converted into phonons and some will be absorbed and re-emitted. Is that correct? I know that my laser has this extremely narrow spectrum...
  44. H

    A Triangulation and Discrete Volume Spectrum in Covariant LQG

    What is often said in Covariant LQG is that the triangulation is a truncation, and is not what is responsible for the discrete volumes one ends up with in the theory. Rather, what is responsible is the discrete spectra of the volume operator acting on the nodes of a spin network. My confusion...
  45. amilton

    I Why does a hydrogen gas tube produce a hydrogen atomic spectrum?

    To measure the atomic hydrogen spectrum people often uses hydrogen gas tubes as light source. Since the gas in the tube is the molecule ##H_2## , why we obtain the spectrum of atomic hydrogen? My guess is that because the voltage is so high, so that the molecules are totally dissociated. If...
  46. rubenhak

    Adding Zooming Capability to my Far Infrared Spectrum Sensor

    Physics noob here. I have the cheapest FLIR sensor (80x60 px sensor). It captures Longwave infrared, 8 μm to 14 μm. It has a tiny lens (probably 1mm in diameter). Trying to add a zoom ability to this sensor. I have different DSLR lens and other optical scopes. I tried holding the tiny FLIR...
  47. arcTomato

    A Average of the power spectrum of Poisson noise

    I am learning about noise that follows a Poisson distribution. When I do a Fourier transform of the data with only Poisson noise to get the power spectrum, what is the average value of the power spectrum?
  48. BohmianRealist

    I Is the phrase "discrete spectrum" in rule #5 a contradiction in terms?

    When conversing informally about QM, there is often wonder about the apparently acausal nature of processes that we may call "quantum leaps" between physical states. It is often said that the purely mathematical foundations of QM give no reason for such wonderment, i.e., that the math, in...
  49. J

    Optical Converting non-visible light to visible spectrum for photography

    I am trying to capture corona discharge on metal conductors. I am using a Canon DSLR and it works pretty good. I think there may be light from outside of the visible spectrum being emitted during these discharge events so I would like to see if it's possible to capture this light and actually...