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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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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Constructing solution to the time-dependent Schrödinger's equation

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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What determines the valid superpostions for a double finite square well?

The following two figures appear in Modern Physics by R. Harris in the chapter Spin and Atomic Physics: Each shows two atoms, represented as finite square wells, and the four lowest-energy (single ...
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Calculating electric field at an uncharged portion in an otherwise uniformly charged sphere

We were doing some problems on electric fields and my teacher discussed this one : Prerequisite: The electric field at a radial distance r inside a uniformly charged sphere of charge density ρ is ...
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Normalized superpositions of two, given at will, coherent states

In many papers it is nicely demonstrated how to prepare in laboratory an arbitrary pure superposition of the two CSS states $(|z\rangle + |-z\rangle)$ and $(|z\rangle- |-z\rangle)$ ($z$ arbitrary ...
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Does the double slit interference pattern depend upon probability?

If the interference pattern depends upon the probability of the particles travelling through the slit then the intensity at any point on the graph must not be zero. But graphs show that the intensity ...
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How does a string store information during wave superposition?

Given we have two Guassian wave pulses in the same medium (string) but in opposite directions. The principle of superposition states that they should pass through each other without being disturbed, ...
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Quantum circuit calculating sum of two quantum states $|a\rangle + |b\rangle$ [closed]

What is the simplest quantum circuit which takes states $|a\rangle$ and $|𝑏\rangle$ as its input, and outputs their (normalized) sum $c (|𝑎\rangle+|𝑏\rangle$)? Here $c$ is a normalization constant ...
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Intuitive explanation for why reflected waves change phase by $π$? [duplicate]

I have seen the equations that show the coefficient of reflection etc. But I'm searching for an intuitive rather than solely mathematical explanation for why waves change phase by π when reflected (...
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How can states be added linearly in a projective Hilbert space?

If you have a Hilbert space $\mathcal{H}$, you can make a projective Hilbert space by modding out by the $U(1)$ group action of multiplying by a phase, $\mathcal{H}/U(1)$. While we usually talk about ...
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How does Pauli's Exclusion Principle relate to a quantum superposition of states?

Pauli's Exclusion principle states 2 fermions can not occupy the same quantum state. However, a particle can occupy a superposition of quantum states. Does this mean you can have an infinite amount of ...
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what will be more appropriate to consider sound wave as a pressure wave or displacement wave

I was reading waves from H.C. Verma in which it was written when two sound sources vibrate in unison then at mid point between the sources a pressure antinode is produced but a displacement node . ...
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Reflection in stationary waves

A stationary wave is formed by the superposition of two waves with the same frequency and amplitude travelling at the same speed in opposite direction. Consider a wave generated by a vibrator is ...
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Double slit experiment with magnetic traps [closed]

Is it possible to perform the following, modified double-slit experiment with single electrons/electron beam: The slits are separated in such a way, that each leads to a separate magnetic trap. The ...
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How to calculate the phase and group velocity of a superposition of sine waves with different speed and wavelength?

This might seem like a trivial question but it is not for me. So, I was reading on group and phase velocities from A.P. French where he calculates the phase and group velocities for a superposition of ...
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Does the angle between adjacent maxima remain the same?

Is the angle between adjacent maxima, in this case adjacent rainbows, the same. That is, is the angle made by the First-order rainbow and Central white the same as the angle made by the First-order ...
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Please show an experiment showing the validity of superposition principle of charges?

I have read in several websites that the superposition principle of electric force has been checked empirically. Can anyone refer/show an experiment (having easy/difficult configurations of charges) ...
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Unnecessary constraint in quantum statistics

In deriving Bose-Einstein or Fermi-Dirac distribution, if $N_n$ is no. of entities with energy $E_n$, then two the constraints for a system with N particles and total energy E are: $\sum_{n=1}^{\...
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$\psi(\vec{\mathbf{r}}, t) = C_1 f(\vec{\mathbf{r}} \cdot \vec{\mathbf{k}}/k - vt) + C_2 g(\vec{\mathbf{r}} \cdot \vec{\mathbf{k}}/k + vt)$

I am currently studying Optics, fifth edition, by Hecht. I was presented with the three-dimensional differential wave equation $$\dfrac{\partial^2 \psi}{\partial x^2} + \dfrac{\partial^2 \psi}{\...
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Why is double slit considered am example of superposition when it's just showing wave nature of particles?

When electrons are individually passed through two slits, the wave function of each electron, after passing through the slits, combine to form an interference pattern. Isn't this just a demonstration ...
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Does opening two slits instead of one reduce the number of photons arriving at a some locations in the bell shape?

Here is something that's been bothering me about quantum superposition: I'd like to know if experiments suggest that opening two slits would decrease the number of photons falling on a region of ...
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A question about superposition (possibly due to the English expressions)

I am currently reading the book ''The Outer Limits of Reason'' and encountered a description about which I am very confused. I am afraid to say, this may be due to the fact that I am not a native ...
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Intuitive explanation why wavelength and slit width affects fringe width in single slit experiment?

I know the formula that shows that wavelength and the fringes' widths are directly proportional in a single slit experiment, but is there an intuitive explanation for this? What about an intuitive ...
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How does the superposition of states come up in Bohmian Mechanics?

In Bohmian Mechanics, it assumes a universal wave field in which particle's motion can be calculated using Newton's law of motion: \begin{equation} m\frac{d^{2}x}{dt^{2}} = - \nabla(V+U) \end{...
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Why there's a displacement node at the closed end of an organ pipe?

Every textbook mentions that there's a displacement node at the closed end of an organ pipe. But the particles in air rapidly strike (or collide) with the closed end this can induce longitudinal ...
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Can we treat superpostion principle of charges as a simple vector addition?

In my physics NCERT class 12 it says that: Superposition principle should not be regarded as obvious or equated with the law of addition of vectors. It says two things: force on one charge due to ...
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Why superposition of energy states is allowed before measurement?

I read that the electron can be in superposition between the ground state and the next higher energy state until we measures it, how is it possible because electron should be at the lowest energy ...
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What are the eigenfunctions of Hamiltonian of a free particle?

From my actual understanding of quantum physics observable are operators, when we measure some observable we will find an eigenvalue of such operator, and the system will collapse in the eigenstate. ...
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Connection between spin angular momentum of a photon and circular polarization of light

Do photons have spin angular momentum only if they are part of a circularly-polarized beam? I suspect that every photon always has spin angular momentum, but in most cases they have a superposition ...
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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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Destructive interference of waves [duplicate]

If 2 waves have the same frequency and amplitude moving over each other but one of them is ahead of the second so that the phase difference is pi "half wave length" so a perfect and complete ...
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Superposition of quantum states when states are rays: well-definedness question

I have some confusion (uncertainty? :)) about the compatibility between states and superposition in quantum mechanics. I give a bit of background context and then ask my question at the end of the ...
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Disappearing electron

I'm sure the answer to this question will be 'no', but I'd really like to understand why/why not. Say a single electron is sent towards a double slit. Some people talk of it 'going through both ...
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Why not use this experiment to test gravity's quantum properties?

If a heavy object $X$ is in superposition, let's say, at two places "at the same time", to which point is the gravitational pull of that object directed to? This can probably not be answered without ...
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Are there any resonant frequency spectra that do not possess any harmonics?

I’m hoping that somebody can help clarify the following passage regarding standing waves and the systems that support them: Many systems that support standing waves have resonant frequency spectra ...
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Is Schrodinger's cat in a true superposition? [closed]

I've been wondering why nobody seems to talk about the gravitational effects of a macroscopic quantum system. In the cat in a box with poison experiment, we consider the cat to be in a dead or alive ...
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Is the quantum dynamics of a system of interacting particles linear or non-linear?

As I understand it, the linearity of quantum mechanics is considered to be an inviolable principle - e.g., this paper - because (among other things) causality would be violated or and/or superluminal ...
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Are the photons traveling between two linear polarizing filters in the “cat state”?

If I have two linear polarizing filters that are at 0º and 45º, then 50% of the photons from a source of non-polarized light will pass through the first first, and 50% of these will pass through to ...
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What are the differences in physics between $( | 0 \rangle + |1\rangle)/\sqrt{2}$ and $( | 0 \rangle - |1\rangle)/\sqrt{2}$?

They are clear mathematically. The first state is the result after a Hadamard gate is applied to 0; the second 1. If we don't measure them, we know nothing about them? If you do, they have the ...
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What would happen if 2 different photons overlap each other while travelling in the same direction?

Imagine 2 photons with same wavelength but from different sources overlap each other and since they don't interact with each other I like to know if there is any changes to their wavelength vs solo? ...
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Is decoherence the reason why a carbon nanotube the size of a soccer ball cannot exhibit wave-like property? [duplicate]

Imagine a hollow ball made of 1 layer of carbon atoms the size of a standard soccer ball, since it is now too big to fit through the double slit am I right to say that it is not in superposition state ...
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Is the monochromatic solution of the free Schroedinger equation a travelling wave? [closed]

When we examine the monochromatic solution of the free Schroedinger equation: $$\psi(t,\mathbf r) = e^{-i\left(\frac{ħk^2}{2m}\right)t}\left(Ae^{i\mathbf{k\cdot r}} + Be^{-i\mathbf{k\cdot r}}\right).$...
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What happens to the energy when two waves completely interfere destructively? [duplicate]

this question has been asked many times and none seem to completely answer or i am unable to understand the answers So let us consider two mechanical transverse waves traveling in opposite directions ...
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Can we tell if a particle has collapsed due to a measurement?

Suppose we have two electrons A and B. My friend measure the spin on electron B the value is +1/2, and he writes on a piece of a paper the value. Electron A has not been measured, so the spin is in ...
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When two waves undergo complete destructive interference then what happens to the energy of the two waves? [closed]

https://physics.stackexchange.com/q/23953 Here the author of the answer mentions that complete destructive interference acts as a mirror . As the potential energy of the ...

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