Questions tagged [superposition]

A basic principle of solutions of *linear* differential (often wave) equations, ensuring that the sum ("superposition") of two solutions is automatically a solution as well. Conversely, solutions (amounting to quantum states in quantum mechanics, since the Schrödinger equation is linear) can be represented as a sum of two or more other distinct solutions, and so can be Fourier/eigenstate resolved to enhance mathematical tractability.

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Schrodinger equation of linear combination of quantum states

We know that the solution for $i\hbar \frac{\partial}{\partial t}|\psi (t) \rangle = H|\psi (t)\rangle $ where $H$ is time-independent Hamiltonian, is $|\psi(t)\rangle = e^{-iHt/\hbar}|\psi(t=0)\...
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Superposition principle for the electric field

I had read somewhere that superposition principle is valid for linear functions, but the electric field is not a linear function, then why is the superposition principle valid for electric field?
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Does the standing wave equation proof require $\ell=Nλ$? [closed]

Consider two identical sources $S_1$ and $S_2$ of waves, separated by a distance $\ell$ (as shown in the figure). The sources produce waves in opposite directions(and towards each other). Now, ...
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References to superpositions of vacua states, for SSB

I would like to read more about this subject, about having an unbroken symmetric superposition of the vaccua (minimum energy state), instead of directly chosing one, for computing SSB as my teachers ...
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Am I in a superposition?

Someone looks at me. Now, they know my position and my momentum, with some uncertainty. Therefore, they haven't measured either my position nor my momentum, since neither is known perfectly. They ...
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Superposition of momentum plane waves for a WF: discrete of continuous?

On the one hand there is a theorem that states that any reasonable wave function $\Psi$ can be written as a superposition of eigenstates of $\hat Q$ (a hermitian operator). So if $\Psi _i$ are the ...
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Coherence and superposition principle - equivalent properties?

I'd like to revisit a question I posted earlier. While I now know what coherence means (and how it can be defined) I still struggle to give an intuitive explanation that goes along with the word "...
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System in Superposition, Subsystem in Eigenstate: are the variables real/determined or non-real/undeterminate?

As far as I can tell, this is all textbook Quantum Mechanics, no interpretations were assumed. Isolated system $S$ is divided into 2 isolated, separable sub-systems: $Particle$ and $Observer$. $...
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On the superposition of forces [closed]

Isn't force just a vector quantity? Don't vectors of the same kind add according to the superposition principle? So why don't all forces obey the superposition principle?
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Superposition v/s Superimposition

What is the difference between 'superposition of waves' and 'superimposition of waves'?
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From discrete to continuous superposition of waves, what happens to omega?

The Wikipedia page on group velocity uses the superposition of two cosines (of slightly different wavenumbers and angular frequencies) to show that group velocity $v_g = \frac{d\omega}{dk}.$ The sum ...
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How to find Intensity in a diffraction experiment? [closed]

Here's my best bet. Let the Intensity of the light at the slit be $I$. Now split the slit into 3 parts. We know at the point of first secondary maxima, two of the adjacent slits interfere ...
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Superposition of EM waves and "magic" behind tuned receiver circuit

I'm struggling to understand how the receiver circuit (eg. FM radio) is able to extract a particular frequency out of the sum of all received frequencies by its antenna? I've checked dozen of websites,...
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Superposition Intuition

As I have understood so far, contrary to classical mechanics, quantum mechanics never gives you the exact position of a 'particle' but only a probability that the particle is in a certain area. Thus ...
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Superposition of waves for changing frequency [closed]

Is this physically correct statement that the "superposition of waves increases with increasing frequency". An increase in frequency means smaller wavelength --> smaller path differences ...
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Energy of a Point at different times in a Standing Wave

Two waves traveling in opposite directions meet to Produce Standing Waves. At Nodes The displacement of one wave is +x and for the other wave, it is -x. Both of which cancel to produce a Node. At this ...
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Why doesn't a standing wave cancel out?

When a wave gets reflected, doesn't its phase change by 180 degrees. So shouldn't a wave and its reflected counterpart get canceled out as their phase differs by 180 degrees?
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Wavefunction superposition state

Before measurement the wavefunction of a quantum particle, eg an electron, evolves in a superposition state. Can the following wavefunction $$\Psi = 1\,\,\lvert \uparrow \rangle + 0 \,\,\lvert \...
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Is there a "measure of nonlinearity" that can be measured when testing quantum mechanics?

For context, I think the comparison to tests of general relativity here is apt. There is the post-Newtonian formalism that has some well-defined parameters that can discriminate between general ...
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Wave packet destructive interference

In Cohen-Tannoudji's Quantum mechanics book, I was reading about an example of a wave packet. The wave function is a superposition of 3 waves with different wave number: $k_0$, $k_0 + \frac{\Delta k}{...
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How can any quantum superposition get produced, given conservation of energy?

Imagine I have a two-level quantum system $Q$ (motivating example: a trapped-ion qubit) where there is some energy difference between the states $\vert 0\rangle_Q$ and $\vert 1\rangle_Q$. Suppose I ...
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Sum of operators on superposition state

I'm a little confused about how a sum of operators acting on a superposition state are worked out. For instance, the superposition of Fock States (photonic) $$\vert \psi \rangle = \alpha \vert 0 \...
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Does it make sense to add eigenstate bras, such as $\langle x|+\langle p|$?

For a given state vector $|\mathcal{S}(t)\rangle$ in a Hilbert space, it's known that we can express it in different bases. For instance, we can express it in the position basis as $\langle x|\mathcal{...
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Symmetry arguments in Gauss law and Superposition [duplicate]

Right now I am working on electrostatics. One of the techniques used is to use coulombs law and superposition in a situation where one can sum the point charges and corresponding fields to get the ...
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Reflection coefficient for acoustic waves for normal incidence

Suppose I have two mediums separated by a boundary at $x=0$. A wave, travelling from left to right, would get partly reflected and partly transmitted. Left of the medium, I can write the total ...
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Is there a limit of size for superpositions?

Can objects be always in superposition if there were no environment for decoherence to occur.
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Quantum Superposition and path length

Q based on Allan Adams' Online Intro to Superposition MIT lecture. His simplification is electrons with two properties Color(PC) (White or Black) and Hardness(PH) (Hard of Soft). If you measure PC ...
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Dirac equation on a superposition

If the following is a solution to the Dirac equation $$(i\gamma^\mu\partial_\mu - m)(\psi_1+\psi_2)=0$$ Therefore after distributing $$(i\gamma^\mu\partial_\mu - m)\psi_1+(i\gamma^\mu\partial_\mu - m)\...
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4 answers
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Why do we observe fringe pattern in single slit diffraction?

I understand that diffraction is the bending of light around sharp edges. Using Huygens' theory, one explains this by imagining a plane wave hitting a slit. Normally, each point on the plane wave ...
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Is the observed Schrödinger's cat still in a superposition?

Person A sets up the Schrödinger's cat experiment with a twist: The box also includes a camera, that streams to the monitor of Person B. When the experiment completes, person B knows if the cat is ...
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Superposition of EM waves [closed]

The following travelling Electromagnetic wave $E_x=0, E_y=E_0 \sin{(\omega t -kx)}, E_z=-2E_0 \sin{(\omega t +kx)}$ is (A) Linearly polarised (B) Elliptically polarised (C) Circularly polarised (D) ...
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Particles composed of square roots?

There are some particles which require square roots when telling their compositions. Mostly mesons, not baryons. e.g. $$ρ^0=\frac{u\bar{u}-d\bar{d}}{\sqrt{2}}.$$ Could you explain me how to make sense ...
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Superposition principle in electrostatics: Experiments

I understand that the superposition principle in electrostatics is consistent with experience and therefore is not very questionable. However, is it possible to perform a direct experimental test of ...
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What do we mean by linear Simple Harmonic Motion?

I am confused by the use of "linear" in SHM. What does linear actually signify in Linear SHM. Does it mean :- That the displacement is linear? (I suppose it isn't since displacement varies ...
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Do photons go through one another?

I just read somewhere that sound could travel through light, and that it can travel even though photons go trought each other. So could anyone explain this to me if they have time?
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Why must operators in QM be linear?

Why must all operators in QM be linear (and therefore able to be represented by matrices). What is the physical reasoning behind this? Is it be possible that the non-unitary nature of quantum collapse ...
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5 votes
1 answer
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What would be the difference in a cancelled out wave, and no wave? [duplicate]

Thinking about waves, superposition, fourier transforms etc, and I realized I am unsure of the difference between looking at a still lake, or me and a friend standing on each side creating perfectly ...
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Superposition principle and fixed positions charges

I am trying to understand this sentence of my course: The superposition principle implies that the net force between any two charges is independent of the presence of other charges. This is true if ...
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Why do multiple forces or wave act together in such a way that one wave/force does not affect the action of other?

In case of force I am referring to principle of physical independence of forces. What is the theoretical proof of it? Is it something just empirical? In case of waves, we get to observe that after ...
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Expected value of the electric field operator in the superposition of two number states

Good morning everyone! I have recently started a course of introductory quantum optics, but unfortunately by quantum mechanics background is not very good - so I'm having some problems when it comes ...
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Superposition of Fock states

Fock states form the most convenient basis of a Fock space. Does it mean that any state of a quantum field (any element of Fock space) can be expressed as a superposition of Fock states? Does this ...
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2 votes
2 answers
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The resultant amplitude of $n$ equal oscillators

There is a summation related to adding effect of many equal equally spaced oscillators. I was reading the first few lines of Feynman's lectures on physics (chapter 30) and the way Feynman did the ...
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How does a superconducting qubit exists in the superposition of $|0\rangle$ and $|1\rangle$ states?

In the presentation of superconducting qubits, it is often said that a non-linear inductor is what allows the present of an anharmonic oscillator. This means that because the difference between the $|...
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Relation between phase velocity and $\delta\omega$ and $\delta k$

I'm trying to find a relation between the phase velocity, $v_p=$$\omega \over k$ and $\delta\omega$ and $\delta k$, of a wave formed by adding the two waves: $$y_1=\cos(k_1 x-\omega_1 t)$$ and $$y_2=\...
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4 votes
1 answer
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Why do electrons in an atom only occupy stationary states, without superposition?

In simple quantum mechanical problems such as the infinite square well, we solve the Time Independent Schrodinger's equation by separation of variable, effectively getting the energy eigenstates of ...
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How does linear combination of two solutions of a second order differential equation have complex coefficients...in case of Simple harmonic motion? [duplicate]

I have searched all the websites but couldn't get the answer...everywhere I am seeing linear combinations with real coefficients..but in case of exponential solution of second order differential ...
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Calculate the Expected Value of an Energy Eigenfunction Superposition

Consider $E_1,E_2,E_3,E_4$ whose eigenfunctions are $\phi_1,\phi_2,\phi_3,\phi_4$ respectively and given $\Psi = \phi_1 - 2\phi_3 +\phi_4$, calculate the expected value of energy in this state. I ...
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How does energy conserve during superposition of wave?

Let's consider two overlaping particles of mechanical wave, since it's a mechanical wave, we can think of it as spring-like so energy of particle $ E= \frac{1}{2} k A^2 $ where A is the amplitude of ...
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How to calculate the amplitude of the sum of two waves that have different amplitude? [closed]

I'm now trying to solve a problem like this. ($x$ denotes position and $t$ denotes time. $a_i, k, \omega, \delta_i$ are all constants.) Given the two waves, $u_1(x,t)=a_1 \sin (kx-\omega t + \...
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Superposition equation for a tilted diffraction grating

When we have a diffraction grating that is tilted at an angle, would the formula d sin θ = mλ still work?
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