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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Can this experimental setup generate a superposition of two distinguishable states?

Is it possible to generate a superposition state, $\hat{b}_1^{\dagger} = (\hat{a}_1^{\dagger}+\hat{a}_2^{\dagger})/\sqrt{2}$, in a way as demonstrated in this figure? Notice that this transformation ...
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Doubt in the completeness of wave function

I am reading about the completeness property of wave function. The following is given about it- The energy eigenstates are complete in the sense that any reasonable wave function $\psi(x)$ can be ...
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Can it be shown in experiment that the momentum (or position) states of the electron and proton in hydrogen are entangled?

The states of the electron and proton in hydrogen are entangled. Which means that the momentum and position of both are entangled. Can this be shown in an experiment, so if you measure the momentum (...
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Schroedinger cat states of the harmonic oscillator

I've found in an article that it is possible to prepare experimentally the superposition of two coherent (quasi-classical) states to obtain the Schroedinger cat state: $$ \left|\psi_{\pm}(t)\right\...
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Addition of Potentials

Say we have a charged shell A (radius $R$) that is present within another charged shell B (radius $2R$). The charged shell A has a net charge $Q$ and the shell B has a net charge $3Q$. Taking shell A ...
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Interference and superposition of waves

In the picture above, black and blue lines are representing waves(mechanical) emerging from the slits(after diffraction). Let us consider that at point A, centre of a bright fringe is located. That ...
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Does superposition principle of electric fields hold for conductors?

Suppose we have two identical oppositely charged spheres separated by some short $ x $ distance, then if we say that superposition principle holds, then at all points in space outside the conductors, ...
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Superposition of waves

Let two waves moving in the direction from $D$ to $B$ and $C$ to $A$. These waves are out of phase at $O$. Then will the particles along $OA$ and $OB$ oscillate? If they do oscillate,then can you ...
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How would an atom look like if we knew where the electrons were? (I know it’s silly) [closed]

So we have the normal depictions of atoms, a nucleus made of spherical protons and neutrons, and orbiting spherical electrons, them we have the fuzzy blob depictions, where there is a center, and then ...
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Wave packet in quantum mechanics?

When we talk about light waves or EM waves, we simply say that the wave packet is the superposition of other waves of different wavelengths. In quantum mechanics, we say the same thing; the ...
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Can superposition principle work with boundary conditions in electromagnetism?

Let's suppose I have two finite lines of charge, each of them at some voltage $V$. The first one would be at $x=0$ and the second one at $x=a$, and each of them has the same length $l$. If I want to ...
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If measurement fixes the state of a quantum system, how do we know that superposition exists?

My very limited understanding of quantum mechanics cannot make sense of the superposition phenomena. It would seem to me like if a measurement makes the wave function of a quantum system collapse, ...
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Why do you add independent solutions when finding a general equation for SHM?

In my physics class, we have an assignment based on simple harmonic motion with the differential equation: $$ \frac{d^2x}{dt^2} + a\frac{dx}{dt} + a^2x = 0 $$ Different parts of the question help us ...
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Can a photon be detected by a “lateral” detector? [closed]

If I direct a laser pointer north and I put a photodetector eastwards (i.e. at $90^\circ$ ), and I wait for a very very long time (in a perfect vacuum if necessary), will the detector ever be ...
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Superposing waves to create visible light

I have a question: Is it possible to create visible light using two other non-coherent waves from the electromagnetic spectrum for example superposing infrared and ultraviolet to create visible light?
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Linear combination of atomic orbitals

For example, I have linear combination of states $$|n,l,m\rangle:~| \psi \rangle = c_1 |2,1,0\rangle + c_2 |2,1,-1\rangle +c_3 |2,1,1\rangle $$. Here $n =2$, $l = 1$, so it's three p-orbitals with ...
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What is proof of principle of superposition of waves on a string?

I was studying waves on a string and there was this 'Principle of Superposition of Waves' which states that the net displacement of a point is equal to the vector sum of displacements caused to the ...
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Coherent and non-coherent sources

As we know, if we superpose two coherent sources of intensities $I_1$ and $I_2$, the resultant intensity is not merely equal to $I_1 + I_2$ but sometimes can be much less and much more than that value....
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Can we say with certainty whether an electron is a particle or a wave?

I read in my physics book (NCERT class 11, page no. 374) that overlapping waves algebraically add to give a resultant wave and it is also mentioned that this superposition principle implies that the ...
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Superposition of two waves [closed]

How can I simplify the superposition of two waves, $\vec{E}_1 = A\sin(kz-\omega t)\hat{x}$ and $\vec{E}_2 = A\sin(-kz-\omega t)\hat{y}$ where $\hat{x}$ and $\hat{y}$ are unit vectors? This is in the ...
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In classical physics (classical electrodynamics), why linearity of Maxwell's equations prevent interaction of electromagnetic waves?

In classical physics (classical electrodynamics), electromagnetic waves don't interact. In quantum mechanics, they could. In this article on light-by-light scattering: https://arxiv.org/abs/1702.01625 ...
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Why does the dependence of Coulomb force on the medium not conflict with the superposition principle?

Why does the dependence of Coulomb force on the medium not conflict with the superposition principle? As I have been told (and checked myself on the web including this website), the Coulomb force ...
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How close do two waves need to be to able to superpose? [closed]

DO two waves need to cross paths to be able to superimpose or can they superpose over a distance?
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Do linear theories have infinitely many solutions?

It is said that, in a linear theory, you can add any number of solutions to still find a solution. So, say I initially found three solutions to a linear theory, and I call them a1, a2, and a3. Now I ...
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Can a neutron act as a wave? Can the wave of light superpose with the wave of neutrons?

Can neutrons act as a wave? and can that wave superpose with wave of a photon? and what are, if any, the required conditions for that phenomenon to happen? Thirdly, if we pass light through completely ...
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Examples of Quantum Superposition for the layman?

I'm trying to introduce Quantum Superposition to high-schoolers, and I feel like it would be nice to start with some real-world examples of where it comes up. I'm hoping for non-contrived examples ...
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Why don't we observe superpositions?

Say we are doing the Stern-Gerlach experiment. Here's my understanding of what decoherence tells us. The particle starts in a superposition of spin up and spin down, but then gets entangled with the ...
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Does the ket $\mid \psi \rangle$ and the ket $ \alpha \mid \psi \rangle$ represent the same state?

To show that the state spin $\frac{1}{2}$ particles get a minus sign under a $2\pi$ rotation the following experiment is made A beam of neutron is divided in two beams $A$ and $B$. The beam $A$ ...
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Why do pianos not produce beats?

Beats occur when two sounds that are close in frequency interfere with each other and produce periodic variation in amplitude - called beats. Piano keys that are next to each other seem to satisfy ...
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Abandoning causality. Tell me it ain't so [closed]

What is the gross oversimplification in this thought example? from Quantum Mischief Rewrites the Laws of Cause and Effect (Quantamagazine) Alice and Bob, the stars of so many thought experiments, are ...
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Is 3 Dissonant sounds considered as Beat Frequency or would it be a different type dissonance? [duplicate]

Earlier Today, I had a conversation for physics and the teacher gave a question stating: Keys "A" and middle "C" were pressed which created a Frequency of 440 Hz, A tuning fork was ...
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Does electric field obey superposition in matter?

Does electric field obey superposition in matter? I know its true in vacuum but I was curious if things change in matter.
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Standard deviation of the Hamilton/energy

I've been working with a task in QM and I'm not quite sure it makes sense to me. We have a particle in an infinite well in a superposition of two energy-eigenstates, $\psi_1$ and $\psi_2$. We first ...
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What do we observe with gravity in a superposition?

In terms of generating superpositions, what have we observed in terms of gravitational effects, or what do we expect to observe (considering how we don't have a quantum theory of gravity)? Or do we ...
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A light problem: What happens when light completely destructively interferes?

So here's the setup. We have a spherical source. It emits a pulse of light in all directions with some wavelength $\lambda$. It reflects off of a spherical mirror that is centered around this source. ...
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What effect do particles in superposition have?

Say, with the double slit experiment, in the space between the slits and the wall, what effect does the particle have on those in the air? Is the momentum so spread out to not be measurable with the ...
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Electric field inside spherical cavity charge density

If there is a non-conducting solid sphere with uniform volume charge density $\rho$ and inside it there is a spherical cavity located outside the center of the sphere, why is it the case that the ...
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Standing waves - why do wavelengths fit perfectly?

When reading about standing waves it is always said that only certain wavelengths are "allowed". I understand that these wavelengths are a requirement for there to be a standing wave due to ...
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Is spacetime entangled with a free particle?

Consider a single free particle. If a spacetime metric satisfies the superposition principle, then the full state of the particle and the spacetime should be $$\sum w_{x,y,z,t}|x,y,z,t\rangle|g_{x,y,z,...
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Unequal superpositions of energy eigenstates in two-state quantum systems?

Two-state quantum systems in a superposition of energy eigenstates oscillate with time between the possible states. If both energy eigenstates contribute with the same amplitude, the oscillation is ...
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Why is Schrödinger's cat in a superposition and not a mixture if you model decay with Fermi's golden rule?

I am teaching quantum information for undergraduate math students and as a perspective I thought it would be cool for them to discuss Schrödinger's cat a bit. More precisely I'd like to come up with ...
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AC circuit and Superposition Theorem

I want to find $\Delta V_{ab}$ for the circuit on the figure I have tried to use the superposition theorem, and then Here I find my first question, because if there is a coil between A and B, then $\...
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Why do we hear beats?

I've learnt quite recently that to hear beats the sources must emit sound in almost near frequencies Here is a scenario I have a two tunning forks and together the produce a beats of frequency 2hz But ...
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What happens if a string with both ends fixed is excited with sinusoidal wave with $\lambda \neq 2 L/n $?

We know that if $\lambda = \frac {2L}{n}$ then stationary waves are formed. So, if a wave generator is connected to the string and we set $\lambda = 2L $ then we will see stationary waves. Maybe we ...
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the measurement problem, what is it that drives the wave function to collapse?

I'm hearing a lot of different solutions to the measurement problem. But what is the right answer? Does consciousness play a role in the collapse of the wave function or is there a different factor at ...
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Induced electric field and electric field due to charges obey superposition?

Say a group of charges and a varying magnetic field exists in some region. We'll have two electric fields,due to the charges and due to the magnetic induction. Does the total electric field equal the ...
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How are linear combination of energy eigenstates solutions to the TISE?

My textbook states that: TISE is a generic eigenvalue problem and the superposition state is not a solution to the TISE. Another part of textbook (in context of infinite square well): The most ...
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Group Velocity Clarification

There is something that confuses me a bit about how group velocity is sometimes introduced and explained. For example, Walter Lewin (great professor) in his lectures uploaded on youtube, explains the ...
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Atom in superposition: is it an atom-photon system, and what is the role of the environment?

Let's assume an atom would get from its ground state $|g\rangle$ to its first excited state $|e\rangle$ by absorbing a single photon. Now, let's assume the atom gets from $|g\rangle$ to $\frac{1}{\...
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Can unitary evolution produce a superposition of wavefunctions, or do wave functions have to be 'created' in a superposition before evolution?

A quantum superposition is a wave function such as : $$ |\psi\rangle = \alpha |\psi_1\rangle + \beta |\psi_2 \rangle $$ Unitary evolution will transfer these states to $|\psi'\rangle \to U|\psi\...

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