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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Asymptotic form of wavefunctions in case of $k$ one-dimensional asymptotic regions

I'm reading the paper Hamiltonian Truncation Study of Supersymmetric Quantum Mechanics, and am struggling to understand some things about section 2. In particular eqn 2.2, and how to think about the ...
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A simple question in quanum mechanics on position and momenum eigenstates

The eigenfunctions (eigenstates) for the momentum of a particle are given by the plane waves $$\phi(x,t) = \sin(kx - \omega t)$$ If we sum a large number of these waves in a range from $0$ to $k_m$, ...
Anky Physics's user avatar
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Is the $n=0$ antinodal line in a double slit experiment constant loudness at all points?

If we assume a normal double-slit experiment with two speakers that produce identical sound waves, is the $n=0$ antinodal line going to have a consistent loudness wherever point on it? As the crest ...
Woo Luke's user avatar
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2 answers
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How does spacetime curve around an object in superposition?

I'm trying to learn quantum mechanics and this is a question that came to mind. I tried searching for it online, but I couldn't find a good answer (or at least one I could understand). From what I ...
maniac's user avatar
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Why a state, $|\Psi\rangle=c_A|\vec{x}_A\rangle+c_B|\vec{x}_B\rangle$, doesn't occur for macro but only for micro objects?

Why are macroscopic objects, for example, a wine glass, never found in a superposition of a position eigenstate localized at $A$ and another localized at $B$? Why does it never exist in a state $|\Psi\...
Solidification's user avatar
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Destructive interference of Gravitational Waves and the Conservation of Energy

Destructive interferences are interesting for a physics student, specifically when checking the Energy Conservation. In the case of destructive EM waves or String waves it is easy to understand where ...
TheFyziker's user avatar
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Relation between classical probability and quantum probability formulae

Assuming superposition state $$ \Psi = C_1 \psi_1 + C_2 \psi_2 $$ ,one can write the expectation value $\langle A \rangle$ of a physical magnitude A as follows $$ \langle A\rangle = P_1 \langle A\...
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Nature of a superposition of states: is it true or only theoretical?

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,...
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Is the Huygens' principle consistent for intersecting wavefronts?

When refraction takes place at the interface of two media, wavefronts can be extended to intersect as below: At point of intersection, light requires no time to travel between the wavefronts. However,...
worksifitdoes's user avatar
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Why does the beam splitter create superposition?

Why does the beam splitter create superposition ? Ok, in a double slit you have 2 holes in a wall, and thus there are 2 ways through which the particle to go. But in a beam splitter where are those 2 ...
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Notation for spatially superposed particle using vacuum modes - Why the state of the particle and vacuum is entangled, not separable?

We have two places, call them Here and There where a particle could be. When the particle isn’t spatially superposed we write its state as $ |1\rangle_{Here}\otimes|0\rangle_{There}$ zero being the ...
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Why does white light appear white?

When I think of white light, I'm imagining a combination of all 7 colors of light but I believe that since light has wave nature I can say that at some point that the probability density of red light ...
Gauransh's user avatar
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How many 'wavelengths of length' can a wave have? [closed]

Since a wavelength, $\lambda$, is the length of a entire cycle How many $\lambda$ (complete cycles) can a composed wave have? I mean, for $n \lambda$, how big can $n$ be? And what does it mean, ...
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How come two electrons interfere?

This is something I have read many times that the double slit experiment done with electrons produce the same pattern that we get with light i.e. the electrons undergo superposition similar to that of ...
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Intuition behind Huygens' Principle?

I have recently started learning about physical or wave optics and one of the initial topics is Huygens' Principle. One part of Huygens' Principle states that every point on the wavefront acts as a ...
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Clarifications on interference of waves

Here is my understanding: Superposition describes the effect of two waves, of the same type, coinciding at a point, stating that the resultant displacement is equivalent to the vector sum of the ...
Quin Gardiner Bax's user avatar
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Semi-classical Quantum Ping-Pong in an infinite well potential

The general one particle state in a simple infinite well of size $L$ is a superposition of all the Hamiltonian eigen-states: $$\tag{1} \psi(x, t) = \sqrt{\frac{2}{L}} \sum_{n = 1}^{\infty} c_n \, e^{-\...
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Does it make sense to talk about 'position' of a standing wave?

In any book that I studied, never saw anything like "position of a wave". Does it have to do anything with quantum particles showing so called "superposition".
Gopal Kaushik's user avatar
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Can other objects feeling the gravitational effect of a particle that is in a state of superposition cause its wavefunction to collapse? [duplicate]

When I feel the slight gravitational pull of one particle that is in a state of superposition and I measure the exact pull at any given instant does the wavefunction collapse? If particle A constantly ...
The Burger King's user avatar
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Determining the specific diffraction lines when 2 monochromatic beams are incident on a diffraction grating [closed]

I am wondering whether it is possible to determine the exact colour permutation for the diffraction lines from only the following given information: "When monochromatic red and monochromatic ...
ben13215's user avatar
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Decoherence paper, incomprehensible claims

I am reading the paper "The quantum-to-classical transition and decoherence" by Maximilian Schlosshauer (https://arxiv.org/abs/1404.2635). I doubt the most basic claims in this paper. The ...
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Ontologically speaking, does single-shot quantum interference occur in pairs of possibilities?

I've been perplexed by the semantics used in Science 329, 418-421(2010), where they state that according to Born’s rule and its square exponent, interference always occurs in pairs of possibilities. ...
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Why does linearity imply no communication between Everettian worlds?

Scott Aaronson said in this interview https://youtu.be/1ZpGCQoL2Rk?t=3255 that the linearity of Schrodinger's equation prevents us from communicating with other Everettian worlds. Why? Is it analogous ...
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Does sound need an odd number of spatial dimensions?

In the book "when Einstein walked with Gödel" the author talks about Edwin A. Abotts "Flatland" stating that one problem which was unattended by Abott is the problem of acoustics ...
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Variance/Standard deviation of an observable on a state that is a linear combination of eigenvectors of that observable

I know that when measuring the standard deviation of an observable the result will be zero if the system is an eigenvector of the observable on which i want to calculate the standard deviation. But ...
AlexM3020's user avatar
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2 answers
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Is superposition a real quantum state or just an unknown [duplicate]

Take the Schrodinger's cat thought experiment, without peeking inside the box the state of the cat is unknown but we know of 2 outcomes which are either alive or dead. Once we decided to peek inside ...
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Superposition of energy levels

When thinking about a "random" atom in space (say a Hydrogen atom), should I assume that the electron is in a ground state (or any particular excited eigenstate) or is it in a superposition ...
archil kitiashvili's user avatar
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On sum of amplitudes in Wave Mechanics

Consider Schroedinger equation, which I write in the form $$ (\mathscr{L}+V)\psi=0$$where $\mathscr{L}$ is the kinetic and time-derivative operator. Now, imagine I have two point sources 1,2 with ...
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What experimental proof of quantum superposition do we have?

My question is both naive and subtle. Naive because I don't know much more than the layman about physics and in particular quantum physics. Subtle because physics is an attempt to model the world, ...
b_habegger's user avatar
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Can two normal 1D waves form a wave packet?

I have a confusion A wave packet is described by the superposition of two wave functions: $$Ψ_1(x,t)=A\sin(k_1x−ω_1t)$$ and $$Ψ_2(x,t)=A\sin(k_2x−ω_2t),$$ where $k_1=2.0×10^6\text{m}^{−1}$, $k_2=3.0×...
Prasoon Raj's user avatar
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Does two same light bulbs produce light of same frequency? [duplicate]

If they do, then why don't we observe interference in normal rooms? And if they don't have the same frequency then why is that so?
SumitBhatt's user avatar
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Circular wave superposition

(Per title, I do mean circular wave, not radial wave.) I'm trying to learn about wave mechanics through some 3D simulations, and I've arrived at an interesting case that I can't seem to answer through ...
Nolnoch's user avatar
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The equation for linear combinations of sinusoidal waves

I was reading Introduction to Electrodynamics by D.J Griffith and in the chapter of Electromagnetic waves, it gives an equation for the representation of any wave in terms of sinusoidal waves. This is ...
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Is Stationary wave actually a Wave?

Okay so by the definition of a wave i.e The osciallatory disturbance in a medium which propogates energy is called as wave..the stationary wave contradicts both the crieteria as it doesnt propogate ...
Pheonix's user avatar
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Why discarding the linear combination of solutions?

In Griffiths's textbook (Introduction to quantum mechanics), part I, 4.1.2, he's solving Schrodinger equation in three dimensions, after separating the variables $Y(\theta, \phi) = \Theta(\theta)\Phi(\...
Arthur's user avatar
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Quantum beats as temporal interferences : whats does that mean?

I've already seen the expression "temporal interference" used to designate these "quantum beats"; often to contrast with the "spatial" interference that would be ...
Husserliana's user avatar
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Why vacuum state is an exception from the general rule of quantum theory?

Based on the double slit experiment we know that in the case of a single particle system the wave function or state vector of position is in a superposition of possibilities before measurement. But ...
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Position of central maxima when source is not in line with the slit

If the source is placed at S1, the central maxima would be at the centre of the screen (in line with the slit). However, if the source is shifted to S2, would this mean that the central maximum shifts ...
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Is the vacuum state in superposition before measurement of its gravity effect?

In the case of a particle system the wave function or state vector is in a superposition of possibilities before measurement. But does this rule apply in the case of vacuum state? Is it in a ...
VVM's user avatar
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Eigenvalues of Superpositions [closed]

First, consider the following superposition of two orthonormal spin states, $|1\rangle$ and $|0\rangle$: $$|\Psi\rangle = \frac{1}{\sqrt{2}}(|1\rangle + |0\rangle)$$ $|\Psi\rangle$ would be an ...
Lory's user avatar
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Why is the 0-order Maxima so wide for a single slit diffraction pattern?

When looking at the graph of single or double slit diffraction graph, I noticed then for single slit the 0 ordered Maxima is twice as wide as compared to the other nth order Maxima. However, for ...
Just want to know more's user avatar
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Doubt about superposition principle [closed]

The superposition position in waves is defined as 'the total displacement produced equals vector sum of individual waves.Given that 2 sources S1 and S2 produce waves who's displacement are y1 and y2 ...
Musical Maestro's user avatar
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Phase difference of standing waves

The phase difference of a standing wave is zero. The above statement is found online when searching about standing waves. However, it doesn't make much sense to me. Consider the above diagram of a ...
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Derivation for the interference of two plane waves

I am trying to understand the derivation for the intensity of two interfering waves. In my textbook, I see this: I am confused by everything on the first line, namely: It seems like we are ...
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Why can't linear combinations of superselection eigenspaces exist?

In his Quantum Mechanics: A Modern Development, Ballentine writes (page 184, second edition) that "It is sometimes asserted that states that would be described by vectors [which are linear ...
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Spin state coefficients in Stern-Gerlach experiment

I'm trying to learn quantum mechanics basics by myself. I've been working on the Stern-Gerlach experiment. Now, positioning two apparatus both along the same direction (first z, then x and y) it is ...
Luke__'s user avatar
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Is QFT linear with respect to superposition of multi-particle states?

I saw other posts such as this one but I don't think it's quite the same question, or even if it is, the answer employs the operator formalism and I'm not sure I follow it. I'm wondering, if you have ...
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Is the superposition of a particle before the collapse of the wave function a relative effect?

From the perspective of an electron in the double slit experiment, does the "rest of the universe" that it is disconnected from behave in the same manner as the electron does in our view? As ...
Helena's user avatar
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How can a system be in superposition when there’s a force associated with it?

Not sure what the best way to word the title would be but I’ll explain further: suppose we’re talking about the double slit experiment. As the electron moves its electric field changes, which exerts a ...
user62783's user avatar
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Understanding the potential step for a particle in 1D

In an exercise, I consider a particle moving from $x=-\infty$ towards a potential step, where $V(x)=0$ for $x\leq 0$ and $V(x)=V_0$ for $x>0$. If we consider the case of $0<E<V_0$, we have; $$...
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