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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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 ...
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3answers
476 views

Understanding quantum entanglement.. help me validate this analogy!

I'm struggling to understand the concept of quantum entanglement. I've distilled my understanding into an analogy, and I need your help to validate it. Here it is: Let's say I receive two envelopes. ...
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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 ...
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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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8answers
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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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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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5answers
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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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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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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 ...
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3answers
686 views

Why does destructive interference not stop a wave?

In this picture, the two waves keep moving even after undergoing destructive interference.
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4answers
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The meaning of Superposition

Is superposition purely conceptual or does it represent some real "thing"? Said another way, is superposition thought to have some tangible physical manifestation or is it simply the lack of physical ...
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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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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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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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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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What's an atomic superstate/superposition, and how is it possible?

What's an atomic superstate/superposition, and how is it possible? I understand the basics - being something can be moving and staying still at the same time; the observer changes the behaviour - but ...
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Is the superposition of stationary states a stationary state? If not, then why not?

I am a beginner in Quantum mechanics and as I understand,the superposition of stationary states is also a solution of time-independent Schrödinger equation (TISE). The wave functions that are the ...
8
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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)\...
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1answer
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Can coherent superpositions of a neutron and antineutron exist?

In my recent post I learned that electric charge is always conserved in contrast to strangeness quantum number, which limits the types of Hadrons that can be build. Furthermore, also different masses ...
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1answer
365 views

Entanglement, superposition, and propositional logic [duplicate]

From what I am understanding, there is entanglement in a system if there is a correlation between elements of that system. For an example that I found, If you have only two cards and know that one is ...
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1answer
693 views

Standing waves due to two counter-propagating travelling waves of different amplitude

Suppose I have two counter-propagating travelling waves of the same frequency but of different amplitude, like the transverse waves produced in a string by partial reflection off an endpoint. I read ...
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1answer
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Classical wave equation - validity

I know that classical wave equation holds for spherical wave fronts. In addition, Huygens' principle states that any wave front is a superposition of many spherical wavelets, so why does the equation ...
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3answers
730 views

If we can prove that superposition exists, then why can't we measure it? [closed]

If we experimentally proved that superposition exists, why can't we test if anything is in a superposition state? This seems like a contradiction because one would think that, if superposition exists, ...
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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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1answer
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What exactly does Aaron D. O'Connell's experiment show?

I watched a TED talk by the scientist Aaron D. O'Connell about actually seeing quantum superposition. The link to the talk is :- http://www.ted.com/talks/...
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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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2answers
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Deriving group velocity

At the introduction to quantum mechanic phase $v_p$ and group $v_g$ velocities are often presented. I know how to derive $v_p$ and get equation: $$ \scriptsize v_p=\frac{\omega}{k}. $$ What i dont ...
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2answers
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Can Quantum Entanglement and Quantum Superposition be considered the same phenomenon?

Quantum entanglement is known to be the exchange of quantum information between two particles at a distance, while quantum superposition is known to be the uncertainty of a particle (or particles) ...
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3answers
593 views

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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1answer
218 views

Non coherence of Fermions and Bosons through $U(1)$

I "know" the textbook answer why we cannot write, $$ |\psi\rangle = a|j=\tfrac{1}{2}\rangle + b|j=1\rangle $$ as "each term in the quantum superposition transforms differently under $U(1)$", $$ U(2\...
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2answers
322 views

Quantum Eraser thought experiment with light photons of distinct color

I tried to recreate the Quantum Eraser experiment into a thought experiment with a few changes. It left me a little perplexed as to what outcomes I should expect. Any help would be appreciated. Lets ...
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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
286 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 a photon always in a state of superposition while traveling through space?

In the double-slit experiment, we emit a photon that is in a state of superposition (wave form) which travels through both slits to interfere with itself. When we measure which slit it went through, ...
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2answers
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Is Schrödinger’s cat misleading? And what would happen if Planck constant is bigger?

Schrödinger’s cat, the thought experiment, makes it seem like as if measurement can cause a system to stop being in a superposition of states and become either one of the states (collapsed). So does ...
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2answers
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Intuitive explanation of the waves superposition

When the two waves collide, why do they pass right through each other? Mathematically it's due to the principle of superposition: the sum of the two solutions of a wave equation is also a solution. ...
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7answers
979 views

Is “quantum superposition” just a fancy way of saying that a system is in one state or another with some probabilities? [duplicate]

When we say that an electron is in a quantum state that is a linear combination of two eigenstates, one with the probability of 75% and the other 25%, what is actually happening? Is the electron "...
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3answers
784 views

Is my baby's gender an example of Schrodinger's cat?

At some time in the conception of a child, gender is determined by the X or Y chromosomes given by the male. This is, from my perception, a random selection, like the decaying atom. Like Schrodinger'...
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3answers
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Classical vs qubits: Superposition

Since a quantum information lecture today I have been wondering what does it really mean for a state to be in superposition? Is this something that is answerable? This is what we learnt (or what I ...
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1answer
364 views

Why superposition is useful just for linear functions?

I saw a problem which said that we have a bar between two walls and we increase the temperature. and as you know walls push a force to the bar so the length of it does not change. in the solution I ...
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2answers
661 views

Why does the superposition principle work in method of images?

Okay, let there be a conducting sphere having radius $a$ initially charged with $Q$ & insulated. Now, $q$ is brought in front of the conductor at $y$ from the center. Now, Jackson in his book ...
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1answer
761 views

Diffraction according to Huygens principle - struggling with the concept of diffraction being caused by small point source wavelets

Huygen's principle states that every plane wave is made up of an infinite number of point sources, and that the constructive interference between each wavelet forms the next wave front, and so the ...
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4answers
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Do multiple electrons exist during superposition?

Wikipedia says: Quantum superposition is a fundamental principle of quantum mechanics that holds that a physical system—such as an electron—exists partly in all its particular, theoretically ...
44
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9answers
7k views

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 ...
12
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3answers
626 views

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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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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3answers
7k views

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}{\...
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1answer
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What is a virtual state?

In quantum mechanics / Raman spectroscopy, what is a virtual state? What is the difference between a virtual state and a superposition of states? Can you simply think of the virtual state as a ...