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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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Static equilibrium of charge in hollow tube

In the Feynman lectures vol II 5-2 it gives an example of a static equilibrium of charges. Where we have a hollow tube in which a charge can move back and forth but not sideways. It states that by ...
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Gravitational wave behavior [duplicate]

My guestion is since we have now detected gravitational waves can gravitational waves go through interference (ie destructive or constructive interference) with each other like other waves?
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Two parallel wires [on hold]

We've got a to parallel wires. We know that on the wire 1 is potential $v_{1}$ beetween its ends, conductivity $σ$, current $I_{1}$, $S$ is cross-section area and $d$ is distance beetween wires, $L$ ...
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What if Schrödinger's cat's meowed?

Sorry if this has been asked (every similar question has a title that basically tags Schrödinger's cat) If after the superposition of the cat being dead and alive at one time was created, and the ...
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Expansion of the infinite square well [on hold]

I was studying the expectation value of the energy of a particle in the groud state of the infinite square well after its expansion in terms of width (from $a$ to $2a$), which is: $$\langle H\rangle= ...
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How does Superposition principle follow from Maxwell's equation's linearity?

It is said that whole of electromagnetism can be completely described by the Maxwell's equations. The thing that intrigues me is that how does superposition principle follow? First, I take an ...
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What is the physical meaning of Hamiltonian eigenstates for a single particle?

Let us assume we have one 2-dimensional quantum system with a Hamiltonian $$H = \sum_{n=1}^2 n \omega \mid n\rangle\langle n\mid$$ Do I understand it correctly when I assume that the eigenstates of ...
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Interference of two wave

We can produce a standing wave by superposition of two waves:one incident $y_1=A \sin{(kx-wt)}$and the other one is reflected $y_2=A \sin{(kx+wt)}$ ; (1)According to my teacher, if the two waves has ...
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What happens to energy when waves cancel out? [duplicate]

So this is basically What happens to the energy when waves perfectly cancel each other? again, but I'm not understanding the answers given (or they don't address what I am confused about) Basically ...
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1answer
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What is the basic difference between beats and stationary (standing) waves?

As far as I know both are formed from interference of 2 waves. And why don't the stationary waves undergo destructive interference? It's a bit confusing.
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Superposition Principle for Electric Fields

If there is a collection of charges $q_1,q_2,q_3....q_n$, and we want to calculate the total Electric Field due to all these charges at a point $P$ ,then the we sum them all up by the principle of ...
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Wave Superposition on a crystal

Does the principle of superposition apply for electromagnetic waves on a crystal? So I know that the principle applies for any wave but I don't understand why some books say that doesn't apply for ...
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When and why does the superposition principle of Coulomb's law fail to hold?

In this lecture, Professor Shankar Ramamurthi says that the superposition principle for force vectors of Coulomb's Law is experimentally observed and is not a product of logical analysis. In fact, the ...
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What happens to the pressure time graph when two musical instruments play at the same time?

I'm learning acoustics for the first time and I'm having trouble picturing what the pressure time graph would look like when two instruments play together. https://newt.phys.unsw.edu.au/music/flute/...
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How do magnetic fields combine?

How do the two fields interact to give the combined field, do they superpose like in waves? And how does this field cause the force on the conductor?
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1answer
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Intensity of fringes in a Double Slit experiment

I have learnt that the intensity of fringes in a double slit experiment depends on the following formula: $$I = 4i\cos^2(\delta/2)$$ But it turn out that the intensity of th consecutive fringe ...
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4answers
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Does polarization happen with single Photon?

I have read that circularly polarized light forms from the superposition of two linearly polarised light. Then is it true that polarisation can't happen with single Photon because it always need at ...
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Double slit experiment- light intensity

The standard explanation for the interference pattern is one of constructive and destructive interference between the light waves from the two slits. But, am I right in thinking that light intensity ...
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2answers
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Interference of Schrödinger's Cat states?

A "Schrödinger's cat state" is a macroscopic superposition state. Quantum states can interfere in simple experiments (such as the Mach-Zehnder/Hong-Ou Mandel/etc). Can Schrödinger's cat states be made ...
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Does the non-linear Schrodinger equation satisfy quantum mechanics rules?

Thinking about the 0+1 dimensional (time-only) non-linear Schrodinger equation: $$i\frac{\partial}{\partial t} \psi(t) =\kappa |\psi(t)|^2 \psi(t).$$ Treating $\psi$ as a wave function instead of a ...
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1answer
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Constructive interference derivation

What is the difference between using $y=A\sin\omega t$ and $y=A\sin(ct-x)$ in a wave formula? I am not a math student and I am not getting this.
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Can Gravitational Waves destructively interfere? [duplicate]

I am doing an investigation for a project in college and I'm wondering if two gravitational waves that are half a phase-out of sync with one another could, in theory, interfere with one another? ...
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Superposition of 2 qubit input with a classical $N$-bit basis state

In a problem I am trying to solve, I'm given 2 qubits in the zero state, i.e. |00>, and a classical bit string describing an $N$-bit basis state, |$\psi$>. I need to make a quantum circuit that ...
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photons have no polarization until they are measured or simply cone shaped and self align?

I saw a video showing "superposition" using polarized filters https://youtu.be/YB4uqpQd2AQ?t=496 Proving that the light waves are orianted in many different angles at the same time. alternate theory: ...
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The superposition principle for linear waves

As far as i've seen, the proof for that principle is to show that, the equation representing linear waves has the perk of being linear, thus if y(x,t) and z(x,t) are solutions of the linear equation,...
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Principle of interference between two waves of same wavelength

We have two waves with the same wavelength that have a path difference. Why does the path length difference have to be an integer multiple of the wavelength in order to obtain constructive ...
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How to figure out if a single photon is in a quantic superposed state or not?

I'd like to know if is it possible to figure out if a single photon is in a quantic superposed state or not (i.e. it is unpolarized or not). I precise that I know it is not possible to discriminate ...
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How can you know an unmeasured quantum particle is in several states at once?

If a quantum particle/system has not been measured/observed yet, how can you know it is in several places/states at the same time?
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Does it make sense to ask: what is the probability of a particle being found in a certain state at time $t>0$?

I am dealing with a problem which involves a quantum system of orthonormal two states, $\left|\nu_1\right>$ and $\left|\nu_2\right>$, which are eigenstates of a time-independent Hamiltonian, ...
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1answer
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Statevector formalism,$|\psi\rangle =c_1|A\rangle +c_2|B\rangle \neq (c_1a_1+c_2b_1)|u_1\rangle +(c_1a_2+c_2b_2)|u_2\rangle $

In statevector formalism suppose two particle $|\psi\rangle =c_1|A\rangle +c_2|B\rangle $ where $|A\rangle =a_1|u_1\rangle +a_2|u_2\rangle , |B\rangle =b_1|u_1\rangle +b_2|u_1\rangle $, but $|\psi\...
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1answer
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How is mass accounted for when a particle is in a superposition? [duplicate]

When dealing with a particle as represented by a probability field, how is mass distributed across the field? Would the mass be averaged across the field?
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4answers
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Schrödinger's cat bra-ket interpretation [closed]

Let $\vert\text{#}\rangle$ be the vector state of the cat, $\vert1\rangle$ the "alive" state, and $\vert0\rangle$ the "dead" state. Using the normalization condition $\langle \text{#}\vert\text{#}\...
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Can two semi-infinite plane waves undergo perfectly constructive interference?

This is building off of a question I asked here. When discussing the linked problem with some friends, the consensus seemed to be that the reason two identical semi-infinite plane waves cannot ...
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2answers
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Three slits experiments [closed]

What is the results of three slits experiments ? What is the difference between it and 2 slits experiments?? How can measure superposition by three slits experiments
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If I was Schrödinger's cat, what would I feel? [closed]

What I'm doing Note before reading: I've made two edits for clarification The first starts at: "To clarify based on answers, I think ya'll are missing the meat of the question:" The second starts ...
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3answers
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Time evolution of eigenstates superposition

If a system is in a state $\psi$ which is superposition of, let's say two, energy eigenfunction, namely $\psi_1$ and $\psi_2$, so that $$\psi(t)=\psi_1e^{-i\omega_1t}+\psi_2e^{-i\omega_2t}$$ (I am ...
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Polarization of light using QM principles [duplicate]

If we have vertical linearly polarized light and if we put it through a polarizing filter oriented at 45 to the vertical, then only half of the light passes through. I am able to intuitively grasp ...
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Can light of different frequencies interfere with each other?

In principle I'm aware of superposition and how it works. Nevertheless I'm not really able to answer the following: Will two light beams of different frequencies interfere with each other? More ...
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Would Schroedinger's cat smell 50% like death? [duplicate]

If we left Schroedinger's cat in a superposition for a week would it begin to start smelling 50% like a dead cat and 50% like a living cat? Would the smell of death immediately disappear if we opened ...
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1answer
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Quantum superposition in density matrix formalism

I was thinking about quantum superposition and stumbled into something that made me quite uncomfortable. Consider a qubit with Hamiltonian eigenstates $|0\rangle$ and $|1\rangle$. To each of these ...
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the conclusion of the color hardness example in quantum mechanics

I have gone through some articles online that describe in very detail about the astonishing results of the color and hardness experiment on electrons. I followed first chapter on Superposition in this ...
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Superposition principle in electrostatics

Poisson's equation in electrostatic does not satisfy the linear superposition principle. Can I say that since Laplacian operator is a non-linear operator so it does not follow the linear superposition ...
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3answers
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What happens in an organ pipe at frequencies other than the harmonics?

I learned that, at frequencies corresponding to harmonics, standing waves are formed. But what actually happens at other frequencies? Won't the reflected wave superimpose with the original wave? Do ...
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1answer
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Destructive Interference of two wave pulses [duplicate]

Suppose two identical transverse wave pulses are travelling towards each other on a string where one is inverted with respect to the other. When they meet, destructive interference will occur and the ...
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1answer
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On Superposition In Diffraction

I am a high school student learning Physics. I am currently learning about diffraction of waves, be it water waves, light waves each, in systems where there are 2 slits for it to diffract through. I ...
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Linear combination of wavefunction

What does plus or minus sign indicate in linear combination of wave functions?
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3answers
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How to interpret a wavepacket in quantum field theory: is it one particle or a superposition of many?

In 'classical' quantum mechanics, a wave packet is a (more or less) localized particle. The wave packet can be expanded in a superposition of plane waves, each with a defined momentum and energy. This ...
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Which-way experiment with electrons

Consider the double-slit experiment done with a stream of electrons, sent individually toward the double-slit screen and detection plate. A moving electron is a moving electric charge, which by ...
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De Broglie Wavelength interpretation

I've just started learning about the double slit experiment (just in the short appendix section in Schroeder's Thermal Physics), and I'm extremely confused by this one thing: In it, out of basically ...
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Finding the expansion coefficients of the decomposition of a 3D Gaussian wavepacket in the eigenfunctions of the Hydrogen atom

I'm having trouble with trying to find the expansion coefficients of a superposition of a Gaussian wave packet. First I'm decomposing a Gaussian wave packet $$\psi(\textbf{r},0) = \frac{1}{(2\pi)^{3/...