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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If we solved the observer effect/problem, doesn't this mean Quantum superposition isn't actually real? [duplicate]

I am nowhere close to a physicist so please correct me anywhere I am wrong From what I understand about the observer effect, when we measure one intrinsic property of an electron such as position, ...
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Sequential Stern-Gerlach experiment

Consider the following diagram: (Sakurai) In the first lecture of MIT OCW Quantum Physics 1, 2013 (https://www.youtube.com/watch?v=lZ3bPUKo5zc), Allan Adams implies that if we remove the barrier on ...
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If two beams with orthogonal polarization states are superimposed, then how to evaluate the phase distribution of final beam?

Let the two input beams have different phase fronts and have orthogonal polarization states (say linearly polarized along x and y direction respectively). If these beams are superimposed, then the ...
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Can two waves interfere head on?

Can two waves (like sound or electromagnetic waves) interfere head on? If yes, and suppose they are out of phase with each other and thus interfere destructively, where does the energy of the waves go?...
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Doesn't the Schrödinger's cat inside the box cause the probability wave function to collapse long before a human opens the box?

My point is that there is no superposition of dead and alive. The cat will cause the probability function to collapse long before we open the box. What am I missing here? Isn't the cat capable of ...
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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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Are superpositions contagious?

Does quantum mechanics really predict that a particle prepared in a state of superposition of spin will result, after being measured by an appropriate instrument (Stern-Gerlach device), in a ...
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Confusion with mixed state [duplicate]

I have read that mixed state is a collection of pure states ...while a pure sate is a collection ie suoerposition of eigen states is that right?..so it can be thought of as a superposition of ...
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Understanding the quantum mechanical state vector

According to Griffiths, there is a general state vector $|s(t)\rangle$ that encodes the state of the system. He also says that we take $\Psi(x, \ t) \ = \ \langle x | s(t) \rangle$. Would then mean ...
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Is the concept of superpositions saying that the electron is actually in many states?

Basically when I read about it, yes. But I don't completely get why. Let me explain: If I throw a ball into a room and don't look, I would surely say that the ball is at one point in this room. Maybe ...
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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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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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Are superposition and time-evolution of a quantum system unrelated?

Consider a single particle (a single qubit if you will) in some arbitrary state $|\psi\rangle$ and an eigenvector $|\lambda\rangle$ corresponding to the eigenvalue $\lambda.$ Consider the time ...
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Do we or do we not observe (measure) superpositions all the time?

This is not a duplicate, the other answers do not specifically solve the contradiction, nor do they give an exact answer. I have read this question: Are we so sure about superposition? How do we ...
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Is there a superposition principle for the motion of interacting charges acted upon by external EM fields?

Consider a system of charges interacting with one another via their EM fields together with external EM fields applied to the system from outside. Suppose we work out the equations of motion ...
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Superposition of gravitational waves and the dark energy

Is it theoretically possible to create a superposition of gravitational waves that form a locally static negative curvature, something like the dark energy?
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Problem in understanding superposition principle in electrostatics

When I have a single charge, it produces a electric field and a test charge will experience a force. Now when I have two(identical,same sign) charges, they produce electric fields and when the test ...
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Formulae for destructive interference [closed]

There are two formulae for destructive interference. In which situation do we use them? $$(n+1/2)\lambda $$ and $$(n-1/2)\lambda $$ I'm confused as my book has mentioned the first one but In ...
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How to understand the makeup of neutral pi and eta mesons?

I know that mesons are bosons made up of quark-antiquark pairs. But when I see the list of mesons, I can see that the makeup of neutral pions and eta mesons are noted in a strange way. $$\pi^0=(u\bar{...
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If we can predict the quantum leap, won't that render quantum computers useless? [duplicate]

Recent news from Yale... We can predict the quantum leap before the particle collapses its superposition. We can even change it to whichever position we like in real time. In layman terms, as I ...
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Confusion about mixed states and pure states

Suppose I have a system composed of two subsystems (each is a 2-state system). I understand, that there exist two types of such systems: separable, and entangled. A separable system can be written as $...
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How can system of charges be static?

I am a beginner in electrostatics. I don't understand the below: When we have a set of charges, those charges exert a force on the test charge but what I don't understand is how are these set of ...
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Is nonlocality more fundamental to quantum theory than superpositions? [closed]

What is more fundamental to quantum mechanics: nonlocality or superpositions?
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Doesn't gravity collapse superposition? [duplicate]

Correct me if I'm wrong, but if you have a proton that is in superposition, you don't know where exactly it is; it is everywhere but with different probability. Couldn't you measure the gravity field ...
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Solution as the real part of a complex exponential from simple harmonic motion

From the book entitled Classical Mechanics written by John R Taylor, chapter no 5, Simple Harmonic Motion. I'm just citing the lines. $$x(t)=\text{Re }Ce^{i\omega t}=\text{Re }A e^{i(\omega t-\...
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Why can $|\Psi (t=0)\rangle $ be written as a coherent superposition of some eigenkets?

Why can $|\Psi (t=0)\rangle $ be written as a coherent superposition of some eigenkets? One of the approaches to solve time dependent Schrodinger equation $i\hbar \frac{\partial |\Psi(t)\rangle}{\...
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Why are all solutions to this system of pendulum differential equations a linear combination of the two given solutions?

I am currently trying to do a lab report for a coupled pendulums experiment in which we find the following linear system of second order differential equations (describing the position as a function ...
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Examples of non-sine waves? [closed]

What would be a non-sine wave? AFAIK, all sound is a sine wave, equally to waves on the sea. What would be a common example of something in nature that's a wave but not a sine wave? Or, would we have ...
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Since pretty much everything is decohered, why we can even made superpositions in the lab at all?

We knew that one reason why most quantum mechanical experiments have to be done in a low temperature and isolated from environment condition is to preserve the coherence required for quantum states to ...
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Fermion Superposition [closed]

In case of superposition of identical particles, we usually just add their amplitudes. For example, if we have several particles having the amplitudes of being in a particular quantum state $\psi_1, \...
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Can any solution to the three-dimensional wave equation be written as a superposition of plane waves?

Can any solution to the three-dimensional wave equation, $$\nabla^2f = \frac{1}{v^2}\frac{\partial^2 f}{\partial t^2},$$ be written as a superposition of sinusoidal plane waves? In "Introduction to ...
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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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Why waves in superposition pass through each other without interference in same medium?

Wave can interact constructively (add up) or destructively (cancel) but how about when they are in a superposition state why is there no interference when they meet up in same medium? Imagine 2 pulses ...
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Destructive interference of light and destroying energy?

I've had a hard time with destructive interference of light, and the possibility of destroying energy. I've read countless articles here and elsewhere, leaving me with the answer of something to the ...
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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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Intensity of the resultant of two complex waves [closed]

Suppose I have two waves: $Y_1= a_1e^{i(wt-kx1)}$ and $Y_2= a_2e^{i(wt-kx2)}$ I know by superposition $Y= Y_1+Y_2$ and intensity $(I) = |Y|² $ But how can I solve it. It seems hard for me to find the ...
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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 reality really epistemological in its complete sense?

Taking the case of Schrodinger's cat, if the measurement of the cat is not yet done, then I don't know whether the cat is dead or alive. Epistemologically speaking, since I don't know about the ...
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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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Interpreting probability densities in atomic orbitals

I once read that an atomic orbital can be conceptualised as a cloud of "electron-ness". That is, the electron literally is the cloud, and the probability density only relates to the probability of the ...
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How do phase shifts affect standing waves?

So I understand that you get standing waves if there are waves of the same amplitude and wavelength traveling in opposite directions. But what happens if the wave traveling in an opposite direction ...
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Does superposition of all possible plane waves represent complete solution of Maxwell's equations in free space?

Consider the set of all possible superpositions of all possible "plane waves that satisfy Maxwell's equations in free space". Does this set represent all possible solutions of Maxwell's equations in ...
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Are there different types of superposition?

In electrostatics or in gravitational, when we are talking about interaction between multiple charges or multiple masses, we say that the interaction between any two charge or mass is independent of ...
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Why can't we superpose two quantum vacuum states?

i read in this paper (Spontaneous Symmetry Breaking as the Mechanism of Quantum Measurement by Michael Grady) that we are not allowed to consider the superposition of two vacuum states. i do not ...
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Deciding amplitude for Beats

I have two harmonic sound waves of nearly equal angular frequencies $\omega_1$ and $\omega_2$, and whose equations(which I have particularly modified for convenience), are $$s_1=a.\cos\omega_1 t$$ $$ ...
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Do “fields” always combine by addition?

"Field" is a fun word which clearly has several meanings. In all fields I can think of in my learning career, the fields obey superposition. I can calculate the fields generated by each object ...
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Why the notion of degree of freedom is correct?

The intuitional definition for number of degrees of freedom is following: it is the minimal amount of numbers which allows us to describe the system's configuration correctly. For example, for dot ...
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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.