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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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Interpreting probability densities in atomic orbitals

I once read that an atomic orbital can be conceptualised as a cloud of "electron-ness". That is, the electron literally is the cloud, and the probability density only relates to the probability of the ...
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How do phase shifts affect standing waves?

So I understand that you get standing waves if there are waves of the same amplitude and wavelength traveling in opposite directions. But what happens if the wave traveling in an opposite direction ...
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Does superposition of all possible plane waves represent complete solution of Maxwell's equations in free space?

Consider the set of all possible superpositions of all possible "plane waves that satisfy Maxwell's equations in free space". Does this set represent all possible solutions of Maxwell's equations in ...
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Are there different types of superposition?

In electrostatics or in gravitational, when we are talking about interaction between multiple charges or multiple masses, we say that the interaction between any two charge or mass is independent of ...
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Why can't we superpose two quantum vacuum states?

i read in this paper (Spontaneous Symmetry Breaking as the Mechanism of Quantum Measurement by Michael Grady) that we are not allowed to consider the superposition of two vacuum states. i do not ...
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Deciding amplitude for Beats

I have two harmonic sound waves of nearly equal angular frequencies $\omega_1$ and $\omega_2$, and whose equations(which I have particularly modified for convenience), are $$s_1=a.\cos\omega_1 t$$ $$ ...
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Do “fields” always combine by addition?

"Field" is a fun word which clearly has several meanings. In all fields I can think of in my learning career, the fields obey superposition. I can calculate the fields generated by each object ...
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Why the notion of degree of freedom is correct?

The intuitional definition for number of degrees of freedom is following: it is the minimal amount of numbers which allows us to describe the system's configuration correctly. For example, for dot ...
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Do quantum superposition occur at sound waves also like at Electromagnetic waves?

Like at the electromagnetic waves we see that they interfers the way like two different wave with frequencies can exist in the same place.
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How can be various frequencies in one place?

How can we receive different radio shows in one place, they are coded in phase or frequency or amplitude of electromagnetic waves, but shouldnt elecreomagnetic waves interact each other, and all ...
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Need help understanding weird definition of pure states [duplicate]

So in many sources I have read that A pure state contains only one element, since the only entry on the density matrix will be 1. But what about superpositions?...
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Does something prevent superposition at our scale?

I often encounter the argument that quantum mechanics reduces to classical mechanics at sufficiently big scales, as soon as h becomes sufficiently small respect to the actions involved. I clearly ...
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Are superposition and uncertainty principles logically dependent?

If we assume superposition and define an Hilbert space with canonical commutation relations we can derive uncertainty relations. So it seems the uncertainty principle isn't required, or should be ...
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Do qubits need to be in superposition to be entangled? [closed]

Do qubits need to be in superposition to be entangled? Put another way, can qubits be entangled but not in superposition?
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Why some forces follow superposition principle?

Let there be a system of $n$ source charges and a test charge $Q$. When we say superposition applies to electrostatic force, we conclude that the interaction between a given source charge and the test ...
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Superposition principle forbids quantisation?

Apparently bound states in quantum mechanics require energy states to be discrete. That means energy in such systems is quantized, right? However, say that we have a superposition of energy ...
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68 views

Are all superposition principles related?

Are all superposition principles related? Is there a relationship between the microscopic superposition principle and the macroscopic superposition principle? Does the microscopic one lend to the ...
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Gauss's Law and Superposition Principle [closed]

Hi I am doing the homework in MIT 8.02 by Dr.Lewin, I doubt that the answer provided online for Problem set is wrong, here is the problem. For question(a)(b)(c) it answers For me, I think the ...
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Why doesn't observing a photon collapse it's wave function into a B or W3 boson?

According to electroweak theory, the photon ($\gamma^0$) and weak bosons ($W^+, W^-, Z^0$) are all linear combinations or superpositions of the weak hypercharge boson ($B$) and the weak isospin bosons ...
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Why do electrostatic potentials superimpose?

I've been trying to convince myself that the assertion that I've read in basic E&M books (Halliday & Resnick, Purcell), and even Griffiths, that the electrostatic potential at a point in space ...
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Confused over the complex term in the simple harmonic wave equation

I am trying to derive the general equation of Lamb wave. My book says that $$y = A\exp(i(kx−\omega t))$$ is the general equation of simple harmonic wave propagating in +ve $x$ direction. but I am ...
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Can quantum black hole be in superposition state?

Quantum black hole can have electric charge and angular momentum or spin, I am wondering if a quantum black hole can be described as a probability wavefunction or not? If so can it quantum tunnels too?...
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Entropy of superposition state vs collapse

Imagine 2 similar atoms one is in superposition state while another is collapse into 1 of the possible States fall into the black hole at the same time, do the 2 atoms lost equal amount of entropy? I ...
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Is the space-time curvature linearly additive?

Could someone please show using equations if space-time curvature due to two bodies being linearly additive or not in general.
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What's the opposite of spin collapse? Superposition as a verb?

With regard to photon spin, I'm trying to figure out what the word is for being "more random" as opposed to collapsing and being "more determined" If I were to say "the spin collapsed", how would I ...
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Why does superposition principle and Copenhagen interpretation not contradict with themselves?

In quantum mechanics, when we say that a particle in a state $|x_1\rangle$, physically the states $|x_1 \rangle $ and $c |x_1\rangle$ (for some $c\not = 0\in \mathbb{C}$) are the same, i.e they ...
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Gravitational wave behavior [duplicate]

My guestion is since we have now detected gravitational waves can gravitational waves go through interference (ie destructive or constructive interference) with each other like other waves?
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What if Schrödinger's cat's meowed?

Sorry if this has been asked (every similar question has a title that basically tags Schrödinger's cat) If after the superposition of the cat being dead and alive at one time was created, and the ...
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Expansion of the infinite square well [closed]

I was studying the expectation value of the energy of a particle in the groud state of the infinite square well after its expansion in terms of width (from $a$ to $2a$), which is: $$\langle H\rangle= ...
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How does Superposition principle follow from Maxwell's equation's linearity?

It is said that whole of electromagnetism can be completely described by the Maxwell's equations. The thing that intrigues me is that how does superposition principle follow? First, I take an ...
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What is the physical meaning of Hamiltonian eigenstates for a single particle?

Let us assume we have one 2-dimensional quantum system with a Hamiltonian $$H = \sum_{n=1}^2 n \omega \mid n\rangle\langle n\mid$$ Do I understand it correctly when I assume that the eigenstates of ...
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Interference of two wave

We can produce a standing wave by superposition of two waves:one incident $y_1=A \sin{(kx-wt)}$and the other one is reflected $y_2=A \sin{(kx+wt)}$ ; (1)According to my teacher, if the two waves has ...
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What happens to energy when waves cancel out? [duplicate]

So this is basically What happens to the energy when waves perfectly cancel each other? again, but I'm not understanding the answers given (or they don't address what I am confused about) Basically ...
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2answers
360 views

What is the basic difference between beats and stationary (standing) waves?

As far as I know both are formed from interference of 2 waves. And why don't the stationary waves undergo destructive interference? It's a bit confusing.
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Superposition Principle for Electric Fields

If there is a collection of charges $q_1,q_2,q_3....q_n$, and we want to calculate the total Electric Field due to all these charges at a point $P$ ,then the we sum them all up by the principle of ...
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Wave Superposition on a crystal

Does the principle of superposition apply for electromagnetic waves on a crystal? So I know that the principle applies for any wave but I don't understand why some books say that doesn't apply for ...
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When and why does the superposition principle of Coulomb's law fail to hold?

In this lecture, Professor Shankar Ramamurthi says that the superposition principle for force vectors of Coulomb's Law is experimentally observed and is not a product of logical analysis. In fact, the ...
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What happens to the pressure time graph when two musical instruments play at the same time?

I'm learning acoustics for the first time and I'm having trouble picturing what the pressure time graph would look like when two instruments play together. https://newt.phys.unsw.edu.au/music/flute/...
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How do magnetic fields combine?

How do the two fields interact to give the combined field, do they superpose like in waves? And how does this field cause the force on the conductor?
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Intensity of fringes in a Double Slit experiment

I have learnt that the intensity of fringes in a double slit experiment depends on the following formula: $$I = 4i\cos^2(\delta/2)$$ But it turn out that the intensity of th consecutive fringe ...
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4answers
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Does polarization happen with single Photon?

I have read that circularly polarized light forms from the superposition of two linearly polarised light. Then is it true that polarisation can't happen with single Photon because it always need at ...
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Double slit experiment- light intensity

The standard explanation for the interference pattern is one of constructive and destructive interference between the light waves from the two slits. But, am I right in thinking that light intensity ...
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2answers
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Interference of Schrödinger's Cat states?

A "Schrödinger's cat state" is a macroscopic superposition state. Quantum states can interfere in simple experiments (such as the Mach-Zehnder/Hong-Ou Mandel/etc). Can Schrödinger's cat states be made ...
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Does the non-linear Schrodinger equation satisfy quantum mechanics rules?

Thinking about the 0+1 dimensional (time-only) non-linear Schrodinger equation: $$i\frac{\partial}{\partial t} \psi(t) =\kappa |\psi(t)|^2 \psi(t).$$ Treating $\psi$ as a wave function instead of a ...
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Constructive interference derivation

What is the difference between using $y=A\sin\omega t$ and $y=A\sin(ct-x)$ in a wave formula? I am not a math student and I am not getting this.
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1answer
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The superposition principle for linear waves

As far as i've seen, the proof for that principle is to show that, the equation representing linear waves has the perk of being linear, thus if y(x,t) and z(x,t) are solutions of the linear equation,...
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Principle of interference between two waves of same wavelength

We have two waves with the same wavelength that have a path difference. Why does the path length difference have to be an integer multiple of the wavelength in order to obtain constructive ...
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How can you know an unmeasured quantum particle is in several states at once?

If a quantum particle/system has not been measured/observed yet, how can you know it is in several places/states at the same time?
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Does it make sense to ask: what is the probability of a particle being found in a certain state at time $t>0$?

I am dealing with a problem which involves a quantum system of orthonormal two states, $\left|\nu_1\right>$ and $\left|\nu_2\right>$, which are eigenstates of a time-independent Hamiltonian, ...
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Statevector formalism,$|\psi\rangle =c_1|A\rangle +c_2|B\rangle \neq (c_1a_1+c_2b_1)|u_1\rangle +(c_1a_2+c_2b_2)|u_2\rangle $

In statevector formalism suppose two particle $|\psi\rangle =c_1|A\rangle +c_2|B\rangle $ where $|A\rangle =a_1|u_1\rangle +a_2|u_2\rangle , |B\rangle =b_1|u_1\rangle +b_2|u_1\rangle $, but $|\psi\...