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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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Physics Superposition

If the width of both slits is increased without changing their separation of a. State the effect of the brightness of the light fringes and dark fringe. The brightness of the light fringe will ...
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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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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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Wave packets not satisfying the Schrödinger equation?

The time-independent Schrödinger equation of a free particle in 1 dimension is $$ \begin{equation} -\frac{\hbar^2}{2m}\partial^2_x\psi(x) = E\psi(x) \end{equation} $$ which has solutions in form of $...
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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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According to the Copenhagen Interpretation what does superposition mean? [duplicate]

I am not interested in Many Worlds Interpretation because I think it’s mental and after some personal research I found out that it wasn’t (despite some claims otherwise) popular among physicists at ...
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Superposition principle in sinusoidal waves

In sinusoidal wave equations that produce interference we simply add their displacements by superposition principle, however superposition position principle can be applied to only linear equations. ...
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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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Why coefficient of states for non-positive Hamiltonian matrix are all non-negative?

For a Hamiltonian $H$, if the all elements of matrix is non-positive under a set of basis $\{|\phi\rangle\}$:$$\langle\phi|H|\phi'\rangle\leq0$$ then the ground state of $H$ will be the linear ...
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How can Schrödinger's cat be both dead and alive? [closed]

So, this goes to something so fundamental, I can barely express it. The Schrödinger's Cat thought experiment ultimately asserts that, until the box is opened, the cat is both dead AND alive. Now, ...
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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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What happens when two opposite EM waves which completely destructs each other hits a wall? [closed]

I have always wondered what happens when two opposite EM waves which completely destructs each other hits a wall? Does it reflects back or does it go through it. Would be good if anyone could give a(...
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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 ...