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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96
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14answers
68k views

What happens to the energy when waves perfectly cancel each other?

What happens to the energy when waves perfectly cancel each other (destructive interference)? It appears that the energy "disappear" but the law of conservation of energy states that it can't be ...
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3answers
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Why do travelling waves continue after amplitude sum = 0?

My professor asked an interesting question at the end of the last class, but I can't figure out the answer. The question is this (recalled from memory): There are two travelling wave pulses moving in ...
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How is quantum superposition different from mixed state?

According to Wikipedia, if a system has $50\%$ chance to be in state $\left|\psi_1\right>$ and $50\%$ to be in state $\left|\psi_2\right>$, then this is a mixed state. Now, consider the state $...
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Extension of Schrödinger's cat thought experiment

My question is quite simple. In the thought experiment of Schroedinger's cat: When the scientist measures the state of the cat, its wavefunction collapses into either the alive or dead state. But ...
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9answers
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If a thousand people whisper inaudibly, will the resulting sound be audible?

If a thousand people whisper inaudibly, will the resulting sound be audible? (...assuming they are whispering together.) I believe the answer is "yes" because the amplitudes would simply add and thus ...
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4answers
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Why is Huygens' principle only valid in an odd number of spatial dimensions?

Apparently Huygens' principle is only valid in an odd number of spatial dimensions: https://mathoverflow.net/a/5396/21349 Huygen's principle in curved spacetimes Why is this? [EDIT] This is ...
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12answers
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How can Schrödinger's cat be both dead and alive? [closed]

So, this goes to something so fundamental, I can barely express it. The Schrödinger's Cat thought experiment ultimately asserts that, until the box is opened, the cat is both dead AND alive. Now, ...
28
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6answers
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Do all waves of any kind satisfy the principle of superposition?

Is it an inherent portion of defining something as a wave? Say if I had something that was modeled as a wave. When this thing encounters something else, will it obey the principle of superposition. ...
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1answer
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Differences between pure/mixed/entangled/separable/superposed states

I am currently trying to establish a clear picture of pure/mixed/entangled/separable/superposed states. In the following I will always assume a basis of $|1\rangle$ and $|0\rangle$ for my quantum ...
22
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5answers
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Linearity of quantum mechanics and nonlinearity of macroscopic physics

We live in a world where almost all macroscopic physical phenomena are non-linear, while the description of microscopic phenomena is based on quantum mechanics which is linear by definition. What are ...
22
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6answers
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Why do electrons in an atom occupy only the stationary states?

When we talk about the elementary problems in quantum mechanics like particle in a box, we first calculate the energy eigen-function. Then we say that the most general state is the linear combination ...
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4answers
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Why is it difficult for water waves to cancel each other?

I have read that destructive interference between water waves always leads to the creation of smaller waves which eventually die out. Why, in particular for water waves, it is hard to cancel each ...
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Schrödinger's cat; why was it necessary?

Could someone please explain to me the idea that Schrödinger was trying to illustrate by the cat in his box? I understand that he was trying to introduce the notion of the cat being both alive and ...
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4answers
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Is water really $H_2O$? On a comment concerning the quantum mechanical description of water made by Hilary Putnam [closed]

I wanted to pose a question here (also posted to r/physics a bit earlier) and was hoping the you all might be able to help. I was re-reading a book by the philosopher Hilary Putnam titled Naturalism, ...
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If a wave function collapses into one state, does it ever go back to a superposition of states?

It is my understanding that after an observation, the wavefunction collapses to one state. Thus, if you do an observation right after an observation (that collapsed the wavefunction), you get the same ...
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4answers
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Is particle superposition reflected in the particle's gravitational footprint?

Recently, I have heard of extensions of the double slit experiment that propose to use a bacterium as the particle. I've also heard that the double slit experiment, in principle, would still show an ...
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2answers
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Why do neutrinos propagate in a mass eigenstate?

I am aware that flavor $\neq$ mass eigenstate, which is how mixing happens, but whenever someone talks about neutrino oscillations they tend to state without motivation that when neutrinos are ...
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4answers
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Does “natural” superposition of particles exist?

While studying the basics of quantum computers, I came across Hadamard gates and learned, that these gates are used to put qubits into superposition meaning that these qubits are both, 0 and 1 at the ...
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If superposition is possible in QM, why do we often assume systems are already in their eigenstates?

My understanding is that an arbitrary quantum-mechanical wavefunction can be written as a linear combination of eigenfunctions of some Hermitian operator, most commonly the Hamiltonian; when a ...
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9answers
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How do we know a quantum state isn't just an unknown classical state?

When an observer causes the wave function of a particle to collapse, how can we know that the wave function was not collapsed already before the measurement? Suppose we measure the z-component of the ...
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What's the difference between an entangled state, a superposed state and a cat state?

1) Can a state be entangled without also being a superposition? (Please give an example.) 2) Can a state be a superposition without being entangled? (Again, an example please.) 3) And what about ...
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Why doesn't superselection forbid almost every superposition?

A superselection rule is a rule that forbids superposition of quantum states. As stated by Lubos here, one cannot superpose states with different charges because of the conservation of charge: An ...
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5answers
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Plants and quantum mechanics!

I have been working on quantum biology and found something interesting that I would like to write an equation for. Scientists have wondered how plants have such a high efficiency in photosynthesis; ...
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Why is the Principle of Superposition true in EM? Does it hold more generally?

In the theory of electromagnetism (EM), why is the principle of superposition true? Can we read it off from Maxwell's equations directly? Does it have any limit of applicability or is it a ...
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3answers
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Can superpositions of baryons with different electric charge and strangeness exist?

I am trying to find out whether the following baryons can exist: $$ |X\rangle = \frac{|u u u\rangle + |d d d\rangle + |s s s\rangle}{\sqrt{3}} $$ $$ |Y\rangle = \frac{|u u u\rangle + |d d d\rangle - ...
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4answers
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Understanding the cause of sidebands in Amplitude Modulation

I've read it many places that Amplitude Modulation produces sidebands in the frequency domain. But as best as I can imagine it, modulating the amplitude of a fixed-frequency carrier wave just makes ...
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2answers
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Can only one particle exist at a defined point in spacetime?

And for the contrasting question, may two or more particles be superimposed at the same point in spacetime?
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Is the Copenhagen interpretation falsifiable?

According to the Copenhagen interpretation, physical systems generally do not have definite properties prior to being measured. The Schrödinger's cat is both dead and alive, until an observation is ...
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3answers
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Quantum Joke (not a real joke, not a riddle)

Supposing I want to make a quantum joke, like writing this on a coffee machine: $$| \text{Status}\rangle = \frac{1}{\sqrt{2}}\ \big( | \text{Working}\rangle \color{red}{\pm} | \text{Down}\rangle \...
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2answers
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Where does energy go in destructive interference? [duplicate]

I have read that when two light waves interfere destructively, the energy contained within is transferred to other parts of the wave which have interfered constructively. However, I am having some ...
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3answers
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What happens when the amplitudes of interfering waves is different in the phenomenon of beats?

I had read that for the formation of beats, two waves must interfere such that they have similar frequencies but not identical, and their amplitudes should be identical. I don't understand why should ...
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3answers
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Determining the probability of outcomes in a measurement

While showing us the Schrodinger's cat experiment, my physics teacher defined: $$\varphi_\text{alive} = \begin{bmatrix}1\\0\end{bmatrix},\qquad \varphi_\text{dead} = \begin{bmatrix}0\\1\end{bmatrix}, ...
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6answers
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Schrödinger's cat and the difficulty of macroscopic superposition state

The Schrödinger's cat was regarded as peculiar since we seldom encounter a superposition state in macroscopic scale: $$ \mid \mathrm{dead \,\,cat} \rangle + \mid \mathrm{alive \,\, cat}\rangle $$ We ...
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3answers
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How is a bound state defined in quantum mechanics?

How is a bound state defined in quantum mechanics for states which are not eigenstates of the Hamiltonian i.e. which do not have definite energies? Can a superposition state like $$\psi(x,t)=\frac{1}{\...
9
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4answers
986 views

Why is classical electromagnetism linear? [duplicate]

When I ask this, I mean it as in when a test charge $q$ is placed in a region that contains two fixed charges $q_1$ and $q_2$, the force acting on it is the vector sum of the forces it would ...
9
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4answers
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Why is quantum entanglement so important in the context of quantum computation?

Entanglement also allows multiple states to be acted on simultaneously, unlike classical bits that can only have one value at a time. Entanglement is a necessary ingredient of any quantum computation ...
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5answers
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Is it correct to say a quantum particle is in both “states” at the same time?

In popular media, and even in introductory books it is common to say that quantum objects are characterized by the non-intuitive notion of being in two or more eigenstates at "the same time". An ...
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2answers
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How does quantum superposition make calculation faster?

In every description of a quantum computer I've seen (that isn't extremely technical), they've been described as computers that use qubits, that use a superposition of 1 and 0 to make processing ...
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3answers
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Schrödinger's cat and Gravitational waves

Schrödinger's cat: a cat, a flask of poison, and a radioactive source are placed in a sealed box. If an internal monitor detects radioactivity (i.e., a single atom decaying), the flask is ...
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5answers
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Can two waves interfere head on?

Can two waves (like sound or electromagnetic waves) interfere head on? If yes, and suppose they are out of phase with each other and thus interfere destructively, where does the energy of the waves go?...
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2answers
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Why is the general solution of Schrodinger's equation a linear combination of the eigenfunctions?

Here is a quote from Introduction to quantum mechanics by David J Griffiths: The general solution is a linear combination of separable solutions. As we're about to discover, the time-independent ...
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1answer
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Difference between phase space and Hilbert space? [closed]

Why is the phase space of classical mechanics not a vector space, but Hilbert space of QM is?
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2answers
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Is it possible that we have a physical state which is a mixture of discrete eigenstates and continuous ones?

For a system has both continuous and discrete spectrum, is it possible that a physical states is something like: $$\psi(x)=\sum_{n=n_1}^{n=n2}c_n\psi_n(x)+\int_{E_0-\Delta_E}^{E_0+\Delta_E}\psi_E(x)\...
8
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1answer
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How to check whether Schrödinger's cat was in superposition of states?

Suppose we can make an arbitrarily precise preparation of a Schrödinger's cat (and isolate it arbitrarily well so that decoherence is not a problem). If we prepare lots of cats in this state, what ...
8
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2answers
201 views

Can't the Higgs vacuum be a superposition?

Supose you have a complex scalar field $\phi$ statisfying the typical Higgs lagrangian \begin{equation} L = \partial_{\mu}\phi\partial^{\mu}\phi + \mu^2\phi^*\phi-\frac{\lambda^2}{2}(\phi^*\phi)^2 \...
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2answers
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Linearity of Quantum Mechanics?

The proof of the No-Cloning Theorem states "By the linearity of quantum mechanics, ..." -- Could someone please give me a rough sketch/outline of what this means? Does it have to do with the Hilbert ...
7
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1answer
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Is the universe linear? If so, why?

I'm trying to build a quantum memory system that uses the superposition principle to model specific phenomenon I am trying to predict. Is the universe linear? The superposition principle would apply ...
7
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3answers
230 views

Is Light intangible to other Light? And how does all the intersecting light exist in space?

I was thinking of how light actually gets into my eyes, and thought about my light bulb shining rays to every part of my bedroom wall, and reflecting them towards me. but then i realized, i could be ...
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4answers
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Is the superposition principle universal?

In David J. Griffiths' Introduction to Electrodynamics, he claims that the superposition principle is not obvious but has always been found to be consistent with the experiments. So I was wondering ...
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1answer
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What is the basis of Huygens principle?

When we were studying mechanical waves like sound waves, and waves on strings in class, we never studied Huygens' principle with these - and nor did we really derive the laws of reflection or ...