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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How do we know that superposition exists? [duplicate]

If I was a god that could see the state of a particle in superposition without touching it, wouldn't I know what the particle is at that moment? Wouldn't that make the superposition concept just ...
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Question about Dirac notation (using the Braket notation) [duplicate]

How do I add two energies and calculate the expectation value given a set state in two $|nlm\rangle$ notation? $|\psi\rangle=\sqrt\frac{1}{2}|n_1l_1m_1\rangle+\sqrt\frac{1}{2}|n_2l_2m_2\rangle$ I know ...
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Does QED evolve unitarily after the Schwinger limit?

If QED becomes nonlinear after the Schwinger limit, shouldn't QED no longer be unitary (above the limit) since linearity is a requirement of a unitary operator (and vice versa)? Does this mean that ...
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'Deriving' superposition representations for 3 particles

I'm trying to write up all the possible superposition states for 3 spin-1/2 particles (one spin-up, 2 spin-down). Lets denote $|\uparrow \rangle = |0\rangle, |\downarrow \rangle = |1\rangle$. ...
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Can two perpendicular beams cancel each other out?

This question is related to the Michelson-Morley experiment. See below an illustration of the setup: When looking at this image, I am wondering where and how exactly the interference occurs. Is it ...
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Has it been practically proven that quantum superposition exists ? If yes, how does it even work?

I was wondering if quantum particles do actually exists in two different states simultaneously and if it has been proven they do indeed exists in a superposition of states. How has it been figured ...
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Understanding Huygens' principle: How is the direction of wave propagation determined? And why there is not destructive interference in every wave?

The Huygens' principle makes me a headache. It sounds ironic to me that many articles say that Huygens' principle helps understand the direction of propagation, and helps understand refraction. When ...
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4answers
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Can viruses be in a superposition? [duplicate]

I know that atoms and entire molecules and even sets of hundreds of molecules can be in superpositions of position eigenstates. Viruses are the smallest living organisms (if they can even be called ...
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Superposition of Microwaves experiment? How does it work?

Please can someone help me out with this experiment and see if this is correct? So the experiment consists of one metal sheet that fully reflects microwaves (and is fixed in its position), and the ...
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1answer
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Amplitude of superposition states

I have a question about the following chart (for 3 and 4 particles case): What does $P_{cycl}$ mean? How's that relevant to the amplitude of superposition states and their symmetricity?
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Wouldn't Gravity Collapse the Wave Function so that Neutrinos have Well-Defined Mass?

My question might be based on a confusion of what counts as a measurement... But anyway the flavour eigenstate of a neutrino is a superposition of mass eigenstates $v_1$ and $v_2$. This is given by: $|...
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What method scientist use to conclude that a particle is on superposition? [closed]

I have seen documentaries, news, and general public reports among other things, that express the conclusion of particles like electrons super position can be at two places at the same time, but i ...
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How is this superposition-of-waves argument correct?

In the fifth edition of Optics Hecht shows that a superposition of wavefunctions (functions that satisfy the wave equation) is a solution to the wave equation. No problem there. He then claims What ...
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Superposition of electromagnetic waves in polarisation

Let's imagine an electromagnetic wave that points every direction (i.e., from $\theta = 0$ to $\theta = 2\pi$). For simplicity let's consider only the electric field vectors. The wave goes through a ...
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1answer
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Bose-Einstein Statistics and Collapse

In Bose-Einstein statistics, two identical bosons can be in one of the following three states with respect to some orthonormal single particle states $|A\rangle$ and $|B\rangle$: (1) $|A\rangle |A\...
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Superposition and Boundary Conditions in Standing Waves

A standing wave is formed due to superposition of two waves with same anplitude, wavelength and period but propagating towards opposite direction to each other. I would like to focus on how initially ...
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1answer
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What is a neutrino state if not a particle?

When reading about the 2015 Nobel prize and how this led to the possibility of the existence of sterile neutrinos I am told that: "(...) three active neutrinos $\nu_e$, $\nu_\mu$, $\nu_\tau$, are ...
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Standing wave and energy conservation

Consider a one-dimensional standing wave formed on the interval $0 \leq x \leq L$. Let's say that this is an ideal model motivated by a string as a medium with both ends closed. Assume that there is ...
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Superposition of state and measuring the linear momentum: what are the possible outcomes?

I have the following wave function (at t=0) which is a superposition of 2 eigenstate, $$ \psi(x,0) = c_0 \sqrt{\frac{2}{L}} \cos\left(\frac{\pi x}{L}\right) + c_1 \sqrt{\frac{2}{L}} \cos\left(\frac{3\...
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In quantum mechanics why do we need the operators to be linear?

In quantum mechanics why do we need the operators to be linear or at best, antilinear?
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The expectation value of the energy of the general wave function in the infinite square well

We know in the infinite square well that the general solution is a linear combination of the stationary states ( states with definite energy eigenvalues). Also the measurement of the energy for that ...
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Why can't photons cancel each other?

The textbook argument against photons canceling each other draws upon the conservation of energy. Does this mean that energy conservation is a "stronger" principle than superposition? Waves ...
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1answer
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Understanding the Double Slit Experiment without Path Integrals

Despite being presented as one of the fundamental results of Quantum Mechanics in practically every textbook, I realized this morning that I don't understand deeply how Quantum Mechanics predicts the ...
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Superposition of two electromagnetic waves and momentum

Electromagnetic waves follows superposition principle. So that we can simply add the fields of waves to calculate the final field. Then let's think there are two waves that are moving through x-axis ...
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Electron superposition in an $m$-level system

I understand second quantization, and how absorption and spontaneous/stimulated emission works for an electron in $m$-level system. In other words, I know how a photon with the right frequency can ...
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1answer
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Does the Stern-Gerlach experiment really suggest superposition?

The Stern-Gerlach experiment is often cited as evidence of quantum superposition and there are some very simple explanations like this one https://www.youtube.com/watch?v=hkmoZ8e5Qn0 in which spin on ...
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Why we add the individuals quantities to find the total amount of a system's “quantity”? Is this by definition of “total”?

Why to find e.g. the total energy of a system of particles (non-interacting) we add their individual kinetic energies? Is total kinetic energy defined to be that sum? It may seem obvious for scalar ...
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Confusion about derivation and application of Jones Vector

I was watching this video (https://www.youtube.com/watch?v=KKQJIMdEEHY) to gain a better understanding about light polarization, but I was having some trouble with the derivation of the Jones Vector. ...
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Question about derivation and application of Jones Vector

I am a quantum computing hobbyist who is trying to learn about photon polarization, specifically about where the Jones vector (used to describe polarization) comes from. I was watching this video (...
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Quantum Entanglement and transfer of time information, is it possible? [duplicate]

If two particles are quantum entangled...let’s call them particle A and particle B. You measure the state of particle A. At this point, can you know the exact time at which the particle B goes from ...
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1answer
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Why would and when do Qubits collapse into one state upon observation?

Something like an electron would act like a particle upon observation because the high energy light waves interfere with it. But what about Qubits? Why do they collapse into one state? And when do ...
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1answer
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Is superposition of charge possible?

Maybe majorana fermions could exist but is very different from both quasi particle pair and particle hole pair, it could have both positive and negative charge in superposition until it is being ...
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If superposition is just uncertainty, then how come quantum computers work? [closed]

If superposition is just uncertainty due to a particle changing on observation and not literally 2 things at once, how come quantum computers work while having qubits that are literally 1 and 0 at the ...
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Defining Superposition

I’d hope to keep this simple. If we decide to measure electron spins along the vertical axis using a Stern-Gerlach device we get an overall even split between up and down. Therefore it is said ...
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What is the reason that Quantum Mechanics is random?

We know quantum mechanics gives a random result when we observe a particle that's in a superposition, but why is it random? One of the explanations I've heard is that because light comes with those ...
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2answers
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Understanding superposition principle

Does the superposition principle actually tell us about our inability to predict what happens during the course of the experiment? Does it tell that, since an experiment has multiple outcomes ( i.e , ...
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1answer
152 views

Is the Schrodinger's Cat experiment possible in principle?

There are already lots of questions (and great answers) regarding Schrodinger's Cat (and Wigner's Friend, which is the same concept) on here. For example, this post is a great explanation of how ...
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Expansion Postulate Quantum Mechanics

How does the expansion postulate allow predictions to be made about measurement outcomes? I understand the postulate as: $$ ψ =\sum_{n} a_n φ_n $$ with coefficients calculated by: $$ a_n =\int φ_n^*...
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Why is quantum measurement not happening all the time? [duplicate]

I have a question which may be very naive yet I have no answer. I studied undergraduate quantum mechanics 4 years ago now and even if I studied more advanced stuff like QFT I feel like I don't ...
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2answers
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Proof of quantum superposition

My question is really very simple, how can one see that a spin 1/2 particle in a definite projection in z(say, up) is in a superposition of Sx states?
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Time-dependent state probability harmonic oscillator [closed]

For my homework i am considering a harmonic oscillator which´s wavefunction at $t=0$ is the superposition of the eigenstates $\psi_n$. $$ \psi(x,t=0) = \sum\nolimits_{n} c_n \cdot \psi_n(x) $$ Now i ...
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Relations between symmetries in sources and fields

I've edited this question way more times that I like to admit. I'll do my best Relation between highly symetric charge distributions and $\nabla\times\mathbf{D}$: In electrostatics, for some charge ...
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1answer
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Quantum mechanically, is superposition a sum or a product?

This question may sound like a no-brainer, but I'm getting confused after watching this lecture (cf. the slide at minute 5:07). The context is to motivate the quantization of a field which, for the ...
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Questions about Schrodinger's cat [duplicate]

While I was listening to my teacher present the basic idea's of Schrodinger's famous thought experiment, he said that because we can not SEE the cat, the cat exists in some sort of position in which ...
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Is it ever possible to test whether an object is in a quantum superposition (versus a mixed state)?

Today I came across a paper, "Experiments testing macroscopic quantum superpositions must be slow," by Mari et al., which proposes and analyzes a thought experiment involving a first mass mA placed in ...
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Representation of wavefunction as superposition of eigenstates

In Quantum Physics it is postulated that, any general state $\psi$ can be represented as superposition of eigenstates with constant coefficients corresponding to any observable. Say, I have all the ...
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The superposition principle in quantum mechanics

This is a question parallel to this question The importance of the phase in quantum mechanics. In introductionary quantum mechanics I have always heared the mantra The superposition principle ...
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Does QM talk about reality in itself or our observation of it? [closed]

I am not a physicist and I've recently started watching introductory lectures on QM on youtube (MIT, Stanford) and reading the Feynman lectures. I have a high-school level knowledge of Math so I'm not ...
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Can you create a stationary/standing wave with two vibrating sources?

In most textbooks, a typical formation of a stationary wave is from a vibrating source in a medium that has a closed-end on the other side. In which the reflected wave will be coherent, with the same ...
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How to write the time-dependent Schrödinger equation from generic functions?

Given the initial state: $$\Psi(x,t=0)=c_1 \psi_1(x)+c_2\psi_2(x)+c_yy(x)$$ where $\psi_1$ and $\psi_2$ are eigenstates of $\hat{H}$ and $y(x)$ is a normalizable function but is not eigenstate of $\...

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