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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46 views

Disappearing electron

I'm sure the answer to this question will be 'no', but I'd really like to understand why/why not. Say a single electron is sent towards a double slit. Some people talk of it 'going through both ...
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Why not use this experiment to test gravity's quantum properties?

If a heavy object $X$ is in superposition, let's say, at two places "at the same time", to which point is the gravitational pull of that object directed to? This can probably not be answered without ...
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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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4answers
187 views

Is Schrodinger's cat in a true superposition? [closed]

I've been wondering why nobody seems to talk about the gravitational effects of a macroscopic quantum system. In the cat in a box with poison experiment, we consider the cat to be in a dead or alive ...
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28 views

Superposition scalar and vector potential and change Maxwell equations

I read some topic about the superposition of electric field and ... but do not mention about scalar and victor potential and superposition. I have a question If I have three electromagnetic fields ...
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1answer
62 views

Is the quantum dynamics of a system of interacting particles linear or non-linear?

As I understand it, the linearity of quantum mechanics is considered to be an inviolable principle - e.g., this paper - because (among other things) causality would be violated or and/or superluminal ...
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Are the photons traveling between two linear polarizing filters in the “cat state”?

If I have two linear polarizing filters that are at 0º and 45º, then 50% of the photons from a source of non-polarized light will pass through the first first, and 50% of these will pass through to ...
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97 views

What are the differences in physics between $( | 0 \rangle + |1\rangle)/\sqrt{2}$ and $( | 0 \rangle - |1\rangle)/\sqrt{2}$?

They are clear mathematically. The first state is the result after a Hadamard gate is applied to 0; the second 1. If we don't measure them, we know nothing about them? If you do, they have the ...
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How can there be a gravintational constant if atomic particles are in superpositions?

Position is one of the measurements when calculating the gravitational force, but atomic particles are in a wave state where position is not known until measured, yet gravity acts on these particles. ...
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1answer
22 views

What would happen if 2 different photons overlap each other while travelling in the same direction?

Imagine 2 photons with same wavelength but from different sources overlap each other and since they don't interact with each other I like to know if there is any changes to their wavelength vs solo? ...
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Is decoherence the reason why a carbon nanotube the size of a soccer ball cannot exhibit wave-like property? [duplicate]

Imagine a hollow ball made of 1 layer of carbon atoms the size of a standard soccer ball, since it is now too big to fit through the double slit am I right to say that it is not in superposition state ...
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112 views

Is the monochromatic solution of the free Schroedinger equation a travelling wave? [closed]

When we examine the monochromatic solution of the free Schroedinger equation: $$\psi(t,\mathbf r) = e^{-i\left(\frac{ħk^2}{2m}\right)t}\left(Ae^{i\mathbf{k\cdot r}} + Be^{-i\mathbf{k\cdot r}}\right).$...
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What happens to the energy when two waves completely interfere destructively? [duplicate]

this question has been asked many times and none seem to completely answer or i am unable to understand the answers So let us consider two mechanical transverse waves traveling in opposite directions ...
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Can we tell if a particle has collapsed due to a measurement?

Suppose we have two electrons A and B. My friend measure the spin on electron B the value is +1/2, and he writes on a piece of a paper the value. Electron A has not been measured, so the spin is in ...
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Quantum mechanics is linear but classical mechanics isn't? [duplicate]

If classical mechanics is a special case of quantum mechanics, how does one account for the fact that the latter is linear when the former isn't? I've asked myself the question after watching this ...
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98 views

When two waves undergo complete destructive interference then what happens to the energy of the two waves? [closed]

https://physics.stackexchange.com/q/23953 Here the author of the answer mentions that complete destructive interference acts as a mirror . As the potential energy of the ...
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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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3answers
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Can physical spaces 'resist' certain sound frequencies?

I whistle a lot, and I'm fairly decent at it. Recently I was walking up the stairs in a house while whistling. As I whistled, I found it difficult to hit a specific note in the song that I would ...
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1answer
50 views

Angular equation for Schrödinger's equation in 3D

In Griffith's book, section 4.1.2, the angular equation for Schrödinger equation in 3D is expressed as $$\sin\theta \frac{\partial}{\partial \theta}(\sin \theta \frac{\partial Y}{\partial\theta})+\...
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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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1answer
106 views

The inflaton field exists in a superposition of energies. How does that affect the rate of cosmological expansion?

The inflaton field is a scalar field that each field value corresponds to different rates of expansion. The field exists in a superposition of energies, that is, the wave function hasn’t collapsed. ...
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1answer
47 views

Does super position precede physical phenomena?

If a traveling wave has amplitude of d, it feels certain amount of force at that moment in time when it is displaced for equilibrium. Thus there is also strain on the string corresponding to that ...
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Does the principle of superposition hold for open quantum systems?

In closed systems, the dynamical equation is the Schrödinger equation, for which the principle of superposition holds. In open quantum systems, does the principle of superposition hold?
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Linear combination of separable solutions of Schrodinger's equation is not an energy eigen function

My doubt was that if a linear combination of separable solutions is also a solution of the Schrodinger's equation, but the linear combination doesn't necessarily satisfy the time independent part, it ...
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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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35 views

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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Theoretically, is macroscopic quantum superposition possible? [closed]

We know that quantum overlap has currently managed to do so in up to 2000 atoms, more and more limits are breaking.
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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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74 views

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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36 views

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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1answer
60 views

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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12answers
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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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1answer
72 views

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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1answer
76 views

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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187 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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1answer
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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199 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) ...