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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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Doesn't gravity collapse superposition?

Correct me if I'm wrong, but if you have a proton that is in superposition, you don't know where exactly it is; it is everywhere but with different probability. Couldn't you measure the gravity field ...
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Solution as the real part of a complex exponential from simple harmonic motion

From the book entitled Classical Mechanics written by John R Taylor, chapter no 5, Simple Harmonic Motion. I'm just citing the lines. $$x(t)=\text{Re }Ce^{i\omega t}=\text{Re }A e^{i(\omega t-\...
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Why can $|\Psi (t=0)\rangle $ be written as a coherent superposition of some eigenkets?

Why can $|\Psi (t=0)\rangle $ be written as a coherent superposition of some eigenkets? One of the approaches to solve time dependent Schrodinger equation $i\hbar \frac{\partial |\Psi(t)\rangle}{\...
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Why are all solutions to this system of pendulum differential equations a linear combination of the two given solutions?

I am currently trying to do a lab report for a coupled pendulums experiment in which we find the following linear system of second order differential equations (describing the position as a function ...
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Examples of non-sine waves? [closed]

What would be a non-sine wave? AFAIK, all sound is a sine wave, equally to waves on the sea. What would be a common example of something in nature that's a wave but not a sine wave? Or, would we have ...
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Since pretty much everything is decohered, why we can even made superpositions in the lab at all?

We knew that one reason why most quantum mechanical experiments have to be done in a low temperature and isolated from environment condition is to preserve the coherence required for quantum states to ...
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Fermion Superposition [closed]

In case of superposition of identical particles, we usually just add their amplitudes. For example, if we have several particles having the amplitudes of being in a particular quantum state $\psi_1, \...
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Can any solution to the three-dimensional wave equation be written as a superposition of plane waves?

Can any solution to the three-dimensional wave equation, $$\nabla^2f = \frac{1}{v^2}\frac{\partial^2 f}{\partial t^2},$$ be written as a superposition of sinusoidal plane waves? In "Introduction to ...
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Probability of finding a particle in a two/three particle system

Let us consider a system of 2 identical particles, 1 and 2. Let, $ψ_a(1)$ is the amplitude of finding particle 1 at state $a$, and $ψ_a(2)$ is the amplitude of finding particle 2 at state $a$. Let N.F ...
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Linearity of Maxwell's equations in tensor formulation

Maxwell equation in tensor formulation are $\partial_\nu F^{\mu \nu}=J^\mu $ and $\partial_{[\gamma} F_{\mu \nu]}=0$. So to show Maxwell equation are linear in vacuum is the following method correct: $...
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How to see linearity of an interaction if it's lagrangian density is known?

The Lagrangian of electrodynamics is $-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}+A_\mu J^\mu$ we know that electrodynamics is linear in special relativity but when we go to general relativity it becomes non-...
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Why waves in superposition pass through each other without interference in same medium?

Wave can interact constructively (add up) or destructively (cancel) but how about when they are in a superposition state why is there no interference when they meet up in same medium? Imagine 2 pulses ...
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Destructive interference of light and destroying energy?

I've had a hard time with destructive interference of light, and the possibility of destroying energy. I've read countless articles here and elsewhere, leaving me with the answer of something to the ...
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Scan Quantum mechanics: Status of current research

I recently stumbled on a new interpretation of Quantum mechanics, called Scan Quantum Mechanics, given by Beatriz Gato-Rivera. She suggests a quantity called quantum inertia, which divides the ...
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Intensity of the resultant of two complex waves [closed]

Suppose I have two waves: $Y_1= a_1e^{i(wt-kx1)}$ and $Y_2= a_2e^{i(wt-kx2)}$ I know by superposition $Y= Y_1+Y_2$ and intensity $(I) = |Y|² $ But how can I solve it. It seems hard for me to find the ...
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Superposition principle in Coulomb's law

My books says that "the principle of superposition is not at all obvious and does not hold in many situations , particularly in the case of very strong electric forces" . Why is that?
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Is reality really epistemological in its complete sense?

Taking the case of Schrodinger's cat, if the measurement of the cat is not yet done, then I don't know whether the cat is dead or alive. Epistemologically speaking, since I don't know about the ...
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Is it possible to compare two systems in superposition?

Is it possible to compare if two systems in a superposition are equal or not equal to each other, i.e. two systems with two electrons in superposition? At first: Superposition of two electrons (...
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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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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 ...