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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Linear combination of eigenstates problem [closed]
Let's say that we have a system such that
$$\Psi(x,0)=\frac{\sqrt3}{2}\phi_1(x)+\frac12\phi_2(x)$$
where both $\phi(x)$ are eigenfunctions of the Hamiltonian operator.
I want to find $\Psi (x,t)$ ...
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Is it valid to add energy densities of *interacting* perfect fluids?
In several papers on interacting perfect fluids in cosmology, the authors assume that we still can add the energy densities and pressures of the individual fluids, as if there wasn't any interaction:
\...
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Physics and Linear Differential Equations
Why in physics, most of the physical systems are modelled by linear differential
equations?
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Why do wave functions need to be normalized? Why aren't the normalized to begin with? [duplicate]
Before I started studying quantum mechanics, I thought I knew what normalization was. Just pulling off Google, here's a definition that matches what I've understood normalization to mean:
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A quantum particle moving from A to B will take every possible path from A to B at the same time
If a quantum particle can take an unlimited number of paths to get from point A to point B wouldn't a quantum particle never get from point A to point B?
A quantum particle takes every path at the ...
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Principle of superposition and QED
For finding a net force on a charge when it is in influence of many charges we simply do vectorical addition of all individual interaction of that charge with others. That's what is principle of ...
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Resultant frequency if 3 harmonic notes (a chord) is played
If I know the frequency of individual notes being played (let's assume D, F# and A), how do I determine the final frequency if they are played (nearly) simultaneously as a chord.
To put the problem ...
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Superimposed state vs. zero amplitude state
Two equal amplitude wave pulses approaching each other through some medium such as a string may form a region of zero amplitude when they overlap completely. At this point, the location of overlap is ...
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Can gravity prevent quantum superposition of positions for a massive object?
Theoretically, nothing prevents a really massive object to be in a superposition of two spatial locations, even far away one from the other. Then I guess spacetime would also show the superposition of ...
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Does it make sense to add eigenstate bras, such as $\langle x|+\langle p|$?
For a given state vector $|\mathcal{S}(t)\rangle$ in a Hilbert space, it's known that we can express it in different bases. For instance, we can express it in the position basis as $\langle x|\mathcal{...
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Can we determine whether a photon's polarization is fixed or in a superposition
Say you have a photon source that produces two kinds of photon,
a photon in a superposition with respect to polarization, |H> + |V>; and
a photon whose polarization is not in superposition, |H> OR |...
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What are the functions of these coefficients $c_1,c_2,c_3,c_4$ in $ \psi_{sp^3}= c_1\psi_{2s}+ c_2\psi_{2p_{x}} + c_3\psi_{2p_y}+ c_4\psi_{2p_{z}}$?
Hybridised orbitals are linear combinations of atomic orbitals of same or nearly-same energies. Atomic orbitals interfere constructively or destructively to give rise to a new orbital which is what we ...
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Can I state that $\Psi (x_1, \dots , x_n,t)= \sum_{i=1}^n a_i \psi (x_i,t) $ via superposition?
Given that the hamiltonian $\hat H$ of a system is a linear operator and $\dot \psi (x_i,t)$ does not depend on spatial coordinates $x_1, ..., x_n$ with bases $\hat e_1, ... , \hat e_n$ can I state ...
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Superposition of quantum states
There has been many questions asked about superposition on this forum, but none of them provided me with a satisfactory answer for my following question.
I understand, quite well, the principle of ...
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Linear and non-linear systems
When I read about the superposition principle, it says that it works only on linear systems, my problem is that I cannot really understand the difference between a linear and a non-linear system. I ...
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Calculating the field of an infinite flat sheet of charge using the superposition principle
I am trying to calculate the field of an infinite flat sheet of charge
(a plain with uniform charge density $\sigma$) using the superposition
principle.
I know that the field of an infinite line ...
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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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Has a photon or electron ever been observed in a state of superposition?
Has subatomic particles ever been seen in a state of superposition or do we just detect information like qubits about the state of the particle? So is actual matter in superposition or is it just ...
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How do three electrons entangle with each other?
In a Quantum entity of two electrons entangled to each other, we know that when one electron's spin is known, then the other electron's spin is the opposite.
But, What's the case in a quantum entity ...
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Interference of Schrödinger's Cat states?
A "Schrödinger's cat state" is a macroscopic superposition state. Quantum states can interfere in simple experiments (such as the Mach-Zehnder/Hong-Ou Mandel/etc). Can Schrödinger's cat states be made ...
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Huygens-Fresnel principle
Huygens principle states that
1) Every point on a given wavefront may be considered as a source of secondary wavelets which spread out with the speed of light in that medium. 2) The new wavefront is ...
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What is the cut-off for quantum superposition?
Is there an explanation as to how macro objects aren't in superposition? At what size do objects stop being in a state of superposition?
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Why do multiple forces or wave act together in such a way that one wave/force does not affect the action of other?
In case of force I am referring to principle of physical independence of forces. What is the theoretical proof of it? Is it something just empirical?
In case of waves, we get to observe that after ...
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The superposition principle in quantum mechanics
This is a question parallel to this question The importance of the phase in quantum mechanics.
In introductionary quantum mechanics I have always heared the mantra
The superposition principle ...
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Are we so sure about superposition?
Apparently particles can be anywhere when not observed. How strong is this theory really? Okay the wave-function can be collapsed through observation but how are we so sure that when an object is not ...
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The Theoretical Minimum: Confusion Over Susskind's Reasoning for mutually orthogonal states
There's a better title for this question but my brain is so fried I can't come up with one.
Important Note: I am a layman, and my understanding of the mathematical concepts of quantum mechanics is ...
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Kim delayed choice experiment
In Kim's delayed choice experiment as described in Wikipedia, you get interference patterns or not depending on whether you look at detectors D3 and D4 (which give you path information) or look at ...
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Why do particles not decohere in their native state?
As I've been trying to wrap my head around the principles of decoherence and quantum behavior I am left wondering why fundamental particles are 'allowed' to exhibit quantum properties even in ideal ...
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What does superposition mean in quantum mechanics?
What does superposition mean in quantum mechanics?
When I say $A+B=C$ (forces). I can mean push something with force $A$ + force $B$ together, and that is same as I push it with force $C$.
But when ...
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Superposition principle forbids quantisation?
Apparently bound states in quantum mechanics require energy states to be discrete. That means energy in such systems is quantized, right? However, say that we have a superposition of energy ...
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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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How is mass accounted for when a particle is in a superposition? [duplicate]
When dealing with a particle as represented by a probability field, how is mass distributed across the field? Would the mass be averaged across the field?
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Direction of wave propagation unchanged after superposition?
It's quite confusing.Principle of superposition states that the amplitude of two superposing wave eqauls their indivisual amplitude vector sum.But what about direction.Souldnt't wave direction of ...
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How are standing waves a result of constructive and destructive interferences?
For constructive I can understand. But destructive I can't.
I can not picture the shape of two pulses or waves maybe that form the resulting standing wave. The places where waves are canceled just ...
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Do photons go through one another?
I just read somewhere that sound could travel through light, and that it can travel even though photons go trought each other. So could anyone explain this to me if they have time?
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Superposition of waves with different initial phase in Quantum Mechanics [closed]
In Quantum Mechanics, if a particle's state is a superposition of many states, then we say that its position is well-defined (by the Heisenberg uncertainty principle, because here we have ill-defined ...
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Confusion in understanding the concept of beats
. . .it is the combined vibration or disturbance basically having the average of the combining frequencies, but with an amplitude that varies periodically with time-one cycle of this variation ...
user36790
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On the field leakage problem in quantum experiments
In a quantum experiment, does the leakage of the electromagnetic fields lead to the suppression of quantum effects? For example if I have an electron in a box, in some quantum superposition. Can I use ...
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Why vacuum state is an exception from the general rule of quantum theory?
Based on the double slit experiment we know that in the case of a single particle system the wave function or state vector of position is in a superposition of possibilities before measurement.
But ...
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Double-Slit experiment and the role of observation in the distribution
so I am still having difficulty understanding the role of measuring/observing the wave function. Many of the videos I have watched says that when we are not looking at the wave function it makes an ...
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Standing waves on string
I am a high school student and I am a little confused about standing waves on string, My confusion is that: we know ,A standing wave is formed by the interference of reflected wave and incident wave ...
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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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Double slit experiment- light intensity
The standard explanation for the interference pattern is one of constructive and destructive interference between the light waves from the two slits.
But, am I right in thinking that light intensity ...
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Constructive interference derivation
What is the difference between using $y=A\sin\omega t$ and $y=A\sin(ct-x)$ in a wave formula?
I am not a math student and I am not getting this.
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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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What do operations on single Qubits of Unfactorable Superpositions Do?
So suppose I have the following Quantum Circuit:
A
---- |Control| -----|Hadamard|----
B
---- |xxxxxxx|------------------------
Which is a 2 input Controlled Gate (applying some gate of two choices ...
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Schrödinger's cat question
what would happen if a CC Camera or videocorder is put along with Schrödinger's cat inside the sealed box? Would it influence the outcome?
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How to calculate the energy of a particle in superposition? [duplicate]
lets say we have particle bc particle bc has a 50/50 odds of either turning into particle b or c
each has energy of 2 units. particle A takes the energy from either b or c depending on the result ...
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Linearity in Quantum Mechanics that make superposition possible
As a beginner in QM, all the video lectures that i have seen talk about superposing wave functions in order to get $\psi$. But from what i know from linear algebra, the system must be linear in order ...
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