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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Is it possible to prepare cat states of light over different frequencies?

Is it possible to form a superposition state of a single photon in multiple frequencies? As an archetypal example, consider the Schrödinger's-cat state $$ |\psi\rangle = |1;\omega\rangle + |1;2\omega\...
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Superposition principle and polarization

I am reading an optics book (Physics of Light and Optics by Peatross and Ware) that asserts this: A beam of light can always be considered as an intensity sum of completely unpolarized light and ...
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'Coherent state' for particle in one-dimensional infinite square well

Is there such superposition of states for particle in given infinite square well ('box') in which all expectation values correspond to classical behavior of particle in this kind of potential: time ...
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Is linearity of the quantum state space a necessary postulate in the reconstruction of quantum theory?

This question is about quantum reconstruction. I am new to this topic, and I decided to read some papers on it. I selected some works which follow an "information-focused" approach. The authors of ...
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Proton as superposition of hadrons: $\vert p\rangle = c_0\vert p_0\rangle+c_1\vert h\rangle+\cdots$

I have a question regarding hadron fluctuations. For instance on page 85 in Feynman's "Photon-Hadron Interactions" equation 15.2 reads: $$\tag1\vert \omega\rangle = \vert \omega_0\rangle+\frac{\...
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420 views

Is it possible to make a destructive interference generator?

Is it possible to make a light source that shifts waves of light to cause destructive interference to cancel the other light source out to make it fully dark?
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Are macroscopic superpositions possible in the presence of gravitational interaction?

Assume that it is possible to prepare a macroscopic system (say a 1kg iron sphere) in a superposition of two position eigenstates 1 meter apart. This experiment has to be isolated from the environment,...
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65 views

Is there a way to measure the degree of superposition of a quantum state?

I am wondering if there is a way to calculate the amount of superposition that a quantum state is in. For example, if I have a $2$-qubit quantum system, with basis $\mathcal{B} = \{|00\rangle, |01\...
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Scan Quantum mechanics: Status of current research

I recently stumbled on a new interpretation of Quantum mechanics, called Scan Quantum Mechanics, given by Beatriz Gato-Rivera. She suggests a quantity called quantum inertia, which divides the ...
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1answer
107 views

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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107 views

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/...
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How to best describe wave behavior on even dimensions?

Main source: http://www.mathpages.com/home/kmath242/kmath242.htm On this article, as far as I understand, the author claims that wave behavior on even dimensions would give rise to many waves with ...
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217 views

Mach-Zehnder interferometer reaction to input light with polarization state ±45˚?

We have a Mach-Zehnder interferometer with two non-polarizing beam splitters. The polarisation state of the input beam is a superposition of +45˚ and -45˚ polarizations. In the upper arm of the ...
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151 views

Can any type of wave produce an interference pattern from two sources?

Can any type of wave produce an interference pattern similar to the one in a double slit experiment? So for example, could a radio wave create an interference pattern through the airwaves?
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Supposing that a quantum system is in a degenerate ground-state, is it valid to call this a “superposition” of the possible groundstates?

According to the adiabatic theorem, a quantum system can be prepared in the ground-state of some Hamiltonian $H_f$ if it starts in the ground state of some Hamiltonian $H_I$ and is varied "slowly" ...
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99 views

Electric potentials and superposition

I had a question regarding the addition of electric potentials. Consider two positively charged particles $q_1$ and $q_2$ at distance $R$ apart. Let the charges have magnitudes $q_1$ and $q_2$. For a ...
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163 views

Why do we use superposition instead of tensor product in interferometer?

In the description of a neutron interferometer here, it says: In an interferometer the incident beam is split into two (or more) separate beams. The beams travel along different paths where they ...
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72 views

Joint wave function of transformed states

Say I have two states, one of which is obtained by transforming the other. If $|\psi_1\rangle$ is the 1st state, then the other state is expressed by: $|\phi_1\rangle=\hat{O}|\psi_1\rangle$ [$\hat{O}$...
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Interpretation of quantum superposition and classical Brownian motion

In the standard, Copenhagen interpretation of quantum mechanics, the usual ontology assigned to the phenomenon that repeated measurements of a quantum mechanical observable yielding different results ...
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Delocalized quantum systems and gravity

Briefly, for microscopic systems be they nano-particles or electrons, that are massive (i.e. rest mass $m_r \neq 0$), we know that their behaviour is described using Quantum Mechanics (QM). Such small ...
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Quantum decoherence and the which way double slit expirment

Using the detector to find which way the particle goes makes the particle become entangled with the detector which destroys coherence meaning the 2 superposition states can't ineract with one another. ...
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278 views

Is there a superposition principle of intensity of light?

If two sources, S1 and S2, of light are shining on a ball, and we are given the formula, L1(P) for the amount of light reflecting off the ball at point P caused by light source S1 and into a pixel, 'p'...
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If a photon is in a early/late superposition how can those states be either in-phase or out-phase?

I'm trying to understand this image. Full article is here. I do understand why the photon after step 1 is in superposition if early and late state. However I don't understand why those states are ...
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188 views

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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Proving law of reflection using Huygens principle

So I was reading the proof of law of reflection using Huygens principle but as I am new on this website so I can't attach a picture,so I will try to explain by writing only. The problem I face is ...
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57 views

QCD-Process with superposition-particle

I am a total beginner with non-abelian gauges. To write down a process from a neutral pion ($\pi^0 = \frac{1}{\sqrt{2}}(u\overline{u}-d\overline{d})$) I expect to have to write it as this ...
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882 views

Superposition and density matrix. What are these states?

I just wanted to understand the following. Let's stay with the harmonic oscillator in QM, just to have an example at hand. First, there are all the different states for $n=1,2,...$. (Let's call them $...
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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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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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If the $E$ component of an EM wave interacts with another $B$ field (from other source), can they generate Poyting vector (or photon flux)?

As shown in the figure, a planar EM wave propagates in the $z$-direction, and its electric component is in the $x$-direction. Meanwhile, in the whole region, there is a static magnetic field B ...
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Group velocity of two cosines

I just encountered the following problem, which is really strange to me. I simply want to calculate the group velocity of the following wave $$F(x,t) = \cos(k_1x) + \cos(k_2x-w_2t).$$ Now I thought, ...
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29 views

Superposed simple harmonic oscillators

When deriving the equation for the superposed amplitude: $$A^2=A_1^2+A_2^2+2A_1A_2 \cos(\phi_2-\phi_1)$$ From $$x_1(t)=A_1 \cos(\omega t+\phi_1)$$and $$x_2(t)=A_2 \cos(\omega t+\phi_2)$$ How do you ...
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How do quantum field values combine?

I am interested in how quantum field values combine under superpositions of states in the case of free real scalar fields. I believe I understand the following: A fock basis of a free real scalar ...
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40 views

Why is resultant displacement in an composition of simple harmonic motion the sum of individual displacements?

I recently came across the concept of the composition in simple harmonic motion. A paragraph says that: If $$x_1 = A_1sin(\omega t)$$ $$x_2 = A_1sin(\omega t + \phi)$$ Then, the resultant ...
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Superimposed Waves

This question has been bothering me for a very long time. Imagine a wire carrying electric current. It carries two alternating current (AC) signals of different frequencies (say $50$ Hz and $60$ Hz). ...
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192 views

Proof of the superposition theorem in linear circuit analysis

I couldn't find a proof of the superposition theorem from circuit analysis anywhere online. I thought it might be helpful to ask and provide my proposed proof as an answer to gather feedback and ...
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201 views

Probability density of time-dependent wave functions

Why is it so that probability density of eigenfunctions of time-dependent schrodinger equation are time independent while that of general wave functions (which are a combination of the eigenfunctions) ...
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153 views

Probability of finding a particle in a two/three particle system

Let us consider a system of 2 identical particles, 1 and 2. Let, $ψ_a(1)$ is the amplitude of finding particle 1 at state $a$, and $ψ_a(2)$ is the amplitude of finding particle 2 at state $a$. Let N.F ...
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Linearity of Maxwell's equations in tensor formulation

Maxwell equation in tensor formulation are $\partial_\nu F^{\mu \nu}=J^\mu $ and $\partial_{[\gamma} F_{\mu \nu]}=0$. So to show Maxwell equation are linear in vacuum is the following method correct: $...
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How to see linearity of an interaction if it's lagrangian density is known?

The Lagrangian of electrodynamics is $-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}+A_\mu J^\mu$ we know that electrodynamics is linear in special relativity but when we go to general relativity it becomes non-...
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Superposition principle in Coulomb's law

My books says that "the principle of superposition is not at all obvious and does not hold in many situations , particularly in the case of very strong electric forces" . Why is that?
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Is it possible to compare two systems in superposition?

Is it possible to compare if two systems in a superposition are equal or not equal to each other, i.e. two systems with two electrons in superposition? At first: Superposition of two electrons (...
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Do quantum superposition occur at sound waves also like at Electromagnetic waves?

Like at the electromagnetic waves we see that they interfers the way like two different wave with frequencies can exist in the same place.
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Entropy of superposition state vs collapse

Imagine 2 similar atoms one is in superposition state while another is collapse into 1 of the possible States fall into the black hole at the same time, do the 2 atoms lost equal amount of entropy? I ...
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What's the opposite of spin collapse? Superposition as a verb?

With regard to photon spin, I'm trying to figure out what the word is for being "more random" as opposed to collapsing and being "more determined" If I were to say "the spin collapsed", how would I ...
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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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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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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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Rules of addition of electric field

According to the principle of superposition of Electric Fields , we know that Electric fields add using laws of vectors. However while adding the electric fields , if for example one field is ...