What is Superposition: Definition and 682 Discussions

The superposition principle, also known as superposition property, states that, for all linear systems, the net response caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually. So that if input A produces response X and input B produces response Y then input (A + B) produces response (X + Y).
A function


{\displaystyle F(x)}
that satisfies the superposition principle is called a linear function. Superposition can be defined by two simpler properties; additivity and homogeneity














{\displaystyle F(x_{1}+x_{2})=F(x_{1})+F(x_{2})\,}


{\displaystyle F(ax)=aF(x)\,}
Homogeneityfor scalar a.This principle has many applications in physics and engineering because many physical systems can be modeled as linear systems. For example, a beam can be modeled as a linear system where the input stimulus is the load on the beam and the output response is the deflection of the beam. The importance of linear systems is that they are easier to analyze mathematically; there is a large body of mathematical techniques, frequency domain linear transform methods such as Fourier and Laplace transforms, and linear operator theory, that are applicable. Because physical systems are generally only approximately linear, the superposition principle is only an approximation of the true physical behavior.
The superposition principle applies to any linear system, including algebraic equations, linear differential equations, and systems of equations of those forms. The stimuli and responses could be numbers, functions, vectors, vector fields, time-varying signals, or any other object that satisfies certain axioms. Note that when vectors or vector fields are involved, a superposition is interpreted as a vector sum. If the superposition holds, then it automatically also holds for all linear operations applied on these functions (due to definition), such as gradients, differentials or integrals (if they exist).

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  1. C

    B How do quantum phenomena affect macroscopic phenomena?

    How do quantum superposition, indeterminacy, tunnelling, and entanglement affect macroscopic phenomena such as tossing a coin, throwing dice, human thoughts, human emotions, decision-making by humans, the behaviour of other sentient animals, photosynthesis, genetic mutation, the speed of light...
  2. K

    A Spontaneous emission and coherence

    Assume I prepare a linear superposition ##\frac{1}{\sqrt{2}}(|g>+|e>)## between a ground and excited level for a large number of "atoms" (it can by any multilevel system, not necessarily an atom). We can assume that the lifetime of the excited level is long enough to allow us to create this...
  3. C

    Alternate form of Principle of superposition

    The definition is, I rewrite it as $$(L[y_1] = L[y_2] = 0) \rightarrow (L[c_1y_1 + c_2y_2] = 0)$$. However, I also wonder, whether it could also be rewritten as, $$(L[c_1y_1 + c_2y_2] = 0) \rightarrow (L[y_1] = L[y_2] = 0) $$ And thus, combining, the two cases, Principle of superposition...
  4. M

    B Origins of the no-cloning theorem

    I was watching this video by minutephysics on the No-cloning theorem. Henry very plainly shows why the no-cloning theorem holds, given the setup. However, I am no quantum physicist and lack the necessary background to truly understand what's going on there. What are the origins of the 3...
  5. billtodd

    I If there ever will be a theory of Quantum Gravity which is testable...

    shouldn't it be a sort of partially GR and partially QM? I mean in a sort of superposition of both theories such that in the specific limit becomes GR and another limit QM, and in the between both regions it's something entirely else, not QM and not GR. Is this possible? I haven't yet done the...
  6. HighPhy

    I About nature of superposition of states

    For quantum mechanics, a certain property of a subatomic particle, e.g. the spin of an electron, which can be either up or down, is a "superposition of states," and one of the two conditions, e.g. the fact that it has spin up or down, doesn't manifest itself until the situation is experimentally...
  7. Z

    Determine Thevenin equivalent circuit.

    Here is the circuit that we need to find the Thevenin equivalent of I am really not confident that the attempted solution below is correct. Let's put a test current source between the terminals we're interested in First let's compute the open circuit voltage. We set the newly introduced test...
  8. B

    B Entanglement & Superposition Probabilities

    I cannot find a clear answer on the following beginner’s question on some QM fundamentals: Suppose we have two particles, A and B. Let’s say we generated these as (or otherwise entangled them as) an entangled pair with opposite/orthogonal states. Perhaps horizontally and vertically polarized...
  9. S

    Exploring Parallel Timelines: A Sci-Fi Mystery of Dreams and Alternate Realities

    I'm working on a story wherein, it seems to the protagonist, he suffered a traumatic event and forgot three years of his life in response to the psychological trauma. Because of physical trauma, doctors medically induced a coma. The forgotten three years include a breakup with his college...
  10. Slimy0233

    B [SOLVED] Regarding the Superposition of Two Plane Waves

    My professor was teaching me about the superposition of two waves and after this derivation, he marked ##2Acos(\frac{dk}{2}x -\frac{d\omega}{2}t)## as the oscillation part and ##sin (Kx-\omega t)## as the oscillation part, I don't understand why? Any answers regarding this would be considered...
  11. F

    Convolution vs Cross-correlation

    Hello, Convolution is essentially superposition. Conceptually, a copy of the same mask/filter is essentially placed at every point in the signal (1D, 2D, ect.). Once all these convolution masks are in place, we just compute the sum and get the convolved signal. The integral formula for...
  12. Ranku

    I Gravitational Force Calculation w/ Superposition Principle

    Consider an object which is constituted of two different materials, which are inseparably mixed together, but which have different magnitude of masses. To calculate the gravitational force of the object upon another object, can the superposition principle be applied to the two constituent...
  13. vibhuav

    I Physical meaning of two independent, non-interacting parts

    I keep coming across this descriptor, "two (or three) independent, non-interacting parts," in many books on QM (for example, Penrose's Shadows of the Mind). It is usually followed by a mathematical description (for example, state vector |A>|B>). I can wrap my mind around the quantum paradox of...
  14. L

    Engineering Solve Superposition Theorem for R1, R2 Circuit

    i have this question and i just want to make sure i am on the right track as i know there are quite a few steps to this to get to the final soultions i need to find Current at r1 voltage at r1 current at r2 voltage at r2 i have so far split this into 2 drawings so i am dealing with one power...
  15. S

    B The Difference Between Wavefunction & Superposition: Exploring Photon Behaviour

    (For me to understand, please be mindful to avoid a bunch of jargon) I'm not sure if the proper word is wavefunction or superposition, and didn't find anything in a search of the difference between the two. So will elaborate on the question in my own words. To begin, as far as I undestand...
  16. P

    Quantum spin superposition interpretation

    Here is my workings out: $$$$ If a particle's spin of magnitude ##\frac {\hbar}{2}## is prepared along direction ##\vec r_1## and subsequently its spin is measured along direction ##\vec r_2 ## at an angle ##\vec \theta ## to ##\vec r_1##, the probability of its being found "spin up" along is...
  17. Isaac0427

    I Superposition of different spins

    Hi all, it has been quite a while since I've been on here. I am curious, as the TLDR summary says, if it theoretically possible to have a particle in a superposition of states with different ##S^2## eigenvalues. For example, a particle being in the state...
  18. orangephysik

    Superposition of two one-dimensional harmonic waves

    ##\mathbf {Homework ~Statement:}## Consider the superposition of two one-dimensional harmonic waves $$s_1(x,t)=3.5 cm \cdot cos(27.5s^{-1} \cdot t - 5.65m^{-1} \cdot x)$$ $$s_2(x,t)=3.5 cm \cdot cos(27.5s^{-1} \cdot t - 5.5m^{-1} \cdot x)$$ ##\mathbf {a)}## Calculate the wavelength ##\lambda##...
  19. M

    I Measurement of a superposition and Born's rule

    Let be a superposition ##|\psi\rangle=\sum_j a_j|j\rangle## with one amplitude ##a_x## much greater than the others, where ##x## is not known. For example, ##|\psi\rangle## may result from the quantum Fourier transform of a periodic wave function with an unknown period. I expect a measurement of...
  20. Yuras

    B Spectral lines and superposition of states

    Let's say atom has two energy levels, ##E_1## and ##E_2##. If atom is in the first state ##|E_1\rangle##, then it's able to absorb a photon with energy ##E_2-E_1##, while transitioning to the second state ##|E_2\rangle##. In atom's spectrum we can see an absorption line at the corresponding...
  21. James1238765

    I Is the superposition of mesons (such as pion) a new particle?

    There are 36 hadron composites composed of 2 quarks selectable from the set ##[u, d, c, s, t, b, \bar u, \bar d, \bar c, \bar s, \bar t, \bar b]## satisfying the condition of having total charge = ##[-1, 0, 1]##. However, the superposition states of pure hadrons are sometimes also listed as new...
  22. R

    B Does the bomb experiment do a measurement?

    In short, the Elitzur–Vaidman bomb experiment consists of a Mach–Zehnder interferometer, where a bomb is placed in one of the paths (I used the wikipedia description https://en.wikipedia.org/wiki/Elitzur%E2%80%93Vaidman_bomb_tester, and Sabine Hossenfelder's video: ) The bomb can be live or a...
  23. F

    B How to evaluate whether a photon's polarization is in superposition?

    Is there an accepted experimental methodology for determining whether a photon's polarization is in superposition or not?
  24. J

    I What is so compelling in the superposition theorem?

    My question is, if the determinism theorem is a good explanation, which covers all holes of the entanglement experiment. why are people still concluding its a 'spooky' superposition which is only determined by a measure and then somehow affects the other measurement. What am I missing? Why is...
  25. E

    B Question about quantum superposition

    All of my speculation is based on my current understanding of quantum physics as an art high school student who just has this as an interest, which is in no way at a quantum physicist's level so I apologize if this question is stupid. Also sorry for my English. Most, if not all of you reading...
  26. link223

    Engineering How to solve this problem by the method of superposition?

    Hello there, I would like to get some help for this problem if possible. The problem here is that, after looking at the table I don't really understand how I'd be able to incorporate the moment at the pin A into the deformation. as if you look at the first page 2nd block, there's that simply...
  27. Jacob Peters

    B Copenhagen Interpretation - Superposition - confirmed?

    Hi, From what I read here, they did a double slit experiment test with neutrons that seemed to confirm superposition that the particle was in both places at once. Thoughts?
  28. G

    I Is it really superposition, or do we just not know its position?

    I have a basic question regarding quantum systems in their potential and defined states: Do quantum systems exist in many possible states (i.e. defined as an uncollapsed wave function) merely because we don’t know what state it’s in (i.e. because we haven’t ‘observed’ or measured it, and...
  29. C

    Understanding the Superposition Principle in Circuit Analysis

    When, if ever, is it necessary to use the superposition principle in order to solve a circuit? Can any circuit with multiple independent voltage sources be solved without superposition?
  30. warhammer

    Intensity Distribution of Superposition of 2 Waves

    We assume incident waves to be: y(1)=y(o)sin(wt) y(2)=3y(o)sin(wt+Φ) As Intensity~(Amplitude)^2 We get y(2)=3y(1) This gives us I(2)=9I(1) We assume I(1)=I(o) & I(2)=9I(o) Resultant Wave Intensity I=I(1)+I(2) +2√(I(1)*I(2))*cosΦ ----> I(o) + 9I(o) + 6I(o)cosΦ (We can take cos of this...
  31. T

    Superposition Principle for two Voltage Sources (confusions about....)

    I have a question about natural limitations when the superposition principle for circuits is applicable. Possibly there is a quite elementary reason why the problem I'm going to present next fails, but up to now I haven't a precise reason why that's exactly the case. Could somebody help...
  32. A

    Engineering Is my method of solving this correct? Superposition theorem

    Hello! Consider this circuit Now I want to calculate the current Ik. The values are given as follows; Uq1 = 12 V Uq2 = 18V R1 = R2 = 8 Ohm R3 = R4 = 20 Ohm My approach was using the Superposition theorem. First I deactived Uq2 and left Uq1 active. Now if I am not mistaken the resistors R2 R3...
  33. entropy1

    I Schrödinger's Cat and radioactive atom

    Particles can be made to be in superposition of their states. Concerning Schrödingers cat, if the cat is in superposition of being dead and alive, does that mean that the atom that drives the narcotic is in superposition of having decayed and not having decayed? And does that mean that any...
  34. MichPod

    I Stern-Gerlach experiment superposition vs mixed state

    Considering SG experiment, it is usually described as if an atom in the end of its path (but before being detected on the screen) is in the superposition state, say, ##|\textsf{spin up}, \textsf{upper path}\rangle+|\textsf{spin down}, \textsf{lower path}\rangle##. Some books (Feynman lectures...
  35. I

    B The superposition of a photon

    When a photon travels through space it is spreading out like a fan while in its superposition (except that it is spreading also vertically in addition to horizontally). So, what happens if for instance the right outer edge of the photon's superposition is captured by the gravity of a black hole...
  36. C

    B How does quantum superposition really work?

    How does putting it potentially inbetween 2 basis states, which U will measure only later, on, do it!? That seems like magic, to me. And yet I accept that it does. Somehow.
  37. C

    B Is quantum superposition involved in the Stern-Gerlach experiment?

    This is how I explain it, away, now: Upon entering the magnetic field the silver atom's valence electron's electric field aligns itself at right angle/s to the magnetic field, the quickest/shortest way it can, as they are wont, to do, somehow, and the rest follows, naturally. And if U are...
  38. sergiokapone

    A Quantum superposition: Is a problem of space-time worldview?

    One of the paradoxical principles in Quantum Physics is the principle of quantum superposition, since in quantum theory we are not really talking about the superposition of waves or oscillations, but about the superposition of states. A classic example demonstrating the phenomenon of quantum...
  39. K

    I Is this system a superposition?

    Suppose a blind man builds a machine that paints three apples with three colors, either red, blue or green. Once the machine has done this, are the three apples in the following superposition: or is the wavefunction just one of It feels like because the man is blind, the apples should be in...
  40. P

    I What is the meaning of superposition of momentum in coherent states?

    Good night. I have a doubt, what is the meaning of the coherent states superposition of momentum? In a many of places, sites I see an explanation for the equations but I never see the explanation between diffences of the superposition of position from momentum.
  41. Krokodrile

    Superposition of two simple harmonic motion

    Hey! I am stuck in this problem, i don't know how to sum this ecuations. I remember that its possible because the direction is the same So, i try to sum like this: cos (t+5325) + 1.5 cos (t+5325) =1.5 cos (t+5325) I don't know if i fine. I thanks your help, please ;)
  42. P

    Principle of superposition for charges/induced charges

    The key observation to solve the above problem is that the charge Q can be dragged out into a flat capacitor plate parallel to the 2 existing plates. Apparently, while the charge distribution on the 2 existing plates changes, the total charge induced on each plate remains the same, due to the...
  43. S

    Engineering Please help me with this circuit question using the superposition theorem

    I have tried many times to solve this network, but can't understand how to get current in each resistors by superposition theorem. Please help me to solve and find currents in each 3 resistors with solution. Note:- The figure is attached below.
  44. Celso

    Superposition in separation method of variables

    Each different boundary condition means a different charge configuration, how can this problem be solved using superposition?
  45. Ali Beladi

    I What does this tricky quantum mechanics equation mean?

    I'm a current high school student and I’m aspiring to become a biochemist. I’m at the moment writing an article about adaptive mutations but there is a lot of tricky quantum mechanics in it which I simply don't get. I have asked everyone and got no answer until someone recommended to ask it in a...
  46. H

    I A statement in a superposition of being true and false?

    If a cat can be in a superposition of being dead and alive, why can't a statement be in a superposition of being true and false?
  47. G

    I How to envision particles in superposition in Many Worlds presplitting

    Should particles in superposition before quantum decoherence (many worlds) be envisioned in the same exact way as they are envisioned before wave function collapse (Copenhagen)? Clearly, the particle in Many Worlds is in a sort of superposition, but with all of the talk about one universal wave...
  48. patric44

    The general equation of the superposition of orthogonal waves?

    hi guys i was trying to derive the general formula of two orthogonal waves $$x^{2}-2xycos(δ)+y^{2} = A^{2} sin(δ)^{2}$$ where the two waves are given by : $$x = Acos(ωt)$$ $$y = Acos(ωt+δ)$$ where ##δ## is the different in phase , i know it seems trivial but i am stuck on where should i begin...