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 ...

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What is the Meaning of the Superposition Principle

I am a bit confused as to what the superposition principle actually means. Does it merely mean that you can express any given state as the linear combination of two vectors? If so, isn't that kind of ...
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0answers
106 views

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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3answers
1k views

Why is a wave pulse a superposition of sine waves?

I have learned that to construct a wave pulse, we need to superimpose multiple sine waves of different frequencies which all interfere to produce the pulse. What I don't understand is that a wave ...
42
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9answers
6k views

Extension of Schrödinger's cat thought experiment

My question is quite simple. In the thought experiment of Schroedinger's cat: When the scientist measures the state of the cat, its wavefunction collapses into either the alive or dead state. But ...
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2answers
66 views

What happens if we measure the two entangled systems of the Bell test simultaneously?

Consider the Bell state $|\psi\rangle =\frac{|00\rangle +|11\rangle}{\sqrt{2}}$. When measuring one of the individual systems, the superposition is projected onto one of the eigenstates $|00\rangle$ ...
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29 views

Standing waves due to two counter-propagating travelling waves of different amplitude

Suppose I have two counter-propagating travelling waves of the same frequency but of different amplitude, like the transverse waves produced in a string by partial reflection off an endpoint. I read ...
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1answer
83 views

What does coherent superposition mean?

There is only one coherent state: $$|\alpha\rangle=e^{-\frac{|\alpha|^2}{2}}\sum_{n=0}^\infty \frac{\alpha^n}{\sqrt{n!}}|n\rangle $$ Also, a pure state does not mean a coherent state. But when does ...
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1answer
51 views

Can a quantum mechanical system have more than one wave-function?

I was told that a quantum mechanical system is completely determined by its wave function. But superposition principle says that given two wave functions of some system, a linear combination of them ...
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2answers
94 views

How to visualize an electron existing in two different places at the same time?

Let's consider a hypothetical situation where there are two electrons. The first electron is in superposition, simultaneously existing in two different locations. Let the locations be ...
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1answer
131 views

Can coherent superpositions of a neutron and antineutron exist?

In my recent post I learned that electric charge is always conserved in contrast to strangeness quantum number, which limits the types of Hadrons that can be build. Furthermore, also different masses ...
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1answer
110 views

Which arrangement of pipe and sources can create a standing wave?

A loudspeaker emitting sound of frequency f is placed at the open end of a pipe of length l which is closed at the other end. A standing wave is set up in the pipe. A series of pipes are then set up ...
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1answer
67 views

Is superposition state of SHO ever observed? [closed]

Feynman says, "It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong." So, is superposition state of Simple ...
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3answers
47 views

When two waves interfere, how to calculate the amplitude of the wave?

As the theory of superposition of waves express the amplitudes of the interfering waves do algebraically sum up. But when we sum up the the total energies of a particle doing a harmonic motion due to ...
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1answer
77 views

Electric field due to a time and space varying current density?

Let us say I have a current density: $$\vec J\equiv\vec J(\vec r, t)$$ This will produce both a time varying magnetic field and a net charge density. Both these effects produce an electric field. If $...
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1answer
49 views

Finding similar quantum superposition pairs [closed]

I am not sure if my thinking is correct and I'd like to ask if someone can confirm it, or give explanation, what am I doing wrong. I did task where I was asked to tell if pairs of expressions for ...
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1answer
58 views

Implications of weak measurement on entanglement

What are the implications of weak-measurement on entangled particles, and how does that resolve the problem of non-superluminal quantum "communication"? If I understand correctly, entangled particles ...
2
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0answers
57 views

Schrödinger's cat experiment in the context of decoherence

I am trying to visualize in more detail the Schrödinger's cat experiment in the context of decoherence. Please let me know if the description below makes sense or is somehow flawed. If the ...
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3answers
34 views

Explanation as to why the sum of two sinusoidal waves, differing by only phase, can be represented by $2y_{m}\cos(\frac{1}{2} \Phi)$

How does the addition of two waves, differing only by phase, collapse to $2y_{m}\cos(\frac{1}{2} \Phi)$? Wouldn't the $\omega$ component of the wave still come into play given that it determines the ...
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1answer
29 views

Is it possible to have two waves of different frequency on one string?

Would this change for different Hz, Wavelengths, Speeds, or amplitudes?
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427 views

Can superpositions of baryons with different electric charge and strangeness exist?

I am trying to find out whether the following baryons can exist: $$ |X\rangle = \frac{|u u u\rangle + |d d d\rangle + |s s s\rangle}{\sqrt{3}} $$ $$ |Y\rangle = \frac{|u u u\rangle + |d d d\rangle - ...
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0answers
32 views

Physical motivation for one dimensional SHM superposition

Are there any real life, simple and mechanical system which motivate the study of Simple Harmonic Motion (SHM) superposition in one dimension? I am preparing a lecture about it but I have not seen any ...
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0answers
53 views

How to draw Feynman diagram for K^- + p -> Sigma^0 + pi^0 — superposition in diagram

I'm trying to draw the Feynman diagram for the reaction $$K^- +p \rightarrow \Sigma^0 + \pi^0$$ I have two problems: How to draw the $\pi^0 = (u\bar u + d\bar d)/\sqrt 2$, a superposition of ...
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2answers
96 views

What is the qualitative difference between quantum superpostion and mixed states? [duplicate]

As I understand it, if one has a complete knowledge of the state of a quantum system (insofar as one knows the statistical distributions of all the observables associated with the state) then one can ...
2
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1answer
54 views

Wavefunction Collapse

I believe my Lecturer and the textbook have contradicted one another. My lecturer gave the example that if the spatial part of the wavefunction of a particle is given by $\psi(x) = c_1\psi_1(x) + c_2\...
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2answers
55 views

Why is a circuit of linear elements itself linear?

A resistor's voltage is proportional to it's current. V=iR. And a source maintains a constant voltage or current. So these are linear, time independent relations. If I put combinations of them in a ...
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1answer
59 views

Physiological Significance of Superposition

To what extent is the concept of superposition appropriate to physiology? In other words, can organisms "actually" exist in a state of superposition?
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2answers
77 views

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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1answer
53 views

Non coherence of Fermions and Bosons through $U(1)$

I "know" the textbook answer why we cannot write, $$ |\psi\rangle = a|j=\tfrac{1}{2}\rangle + b|j=1\rangle $$ as "each term in the quantum superposition transforms differently under $U(1)$", $$ U(2\...
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1answer
49 views

Failure of Superposition principle at high amplitudes

Why does superposition principle fail at high amplitudes. Please answer with respect to transverse waves. If possible, plane progressive transverse waves at best.
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1answer
72 views

Why does phase of a wave change after reflecting from a denser medium?

Why does phase of a wave change when reflected from a denser medium, but no change takes place in phase during transmission?
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2answers
65 views

Linear Combinations of Energy Eigenfunctions in 1D

Given that a particle is in a state defined by the wavefunction: $$\Psi (x,t) = \psi_0(x)e^{-iE_0t/\hbar}+\psi_1(x)e^{-iE_1t/\hbar}$$ where $\psi_0(x)$ and $\psi_1(x)$ are the energy eigenfunctions of ...
3
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1answer
53 views

Is QC with Superpositioned Quantum Gates any different than normal Quantum Computation?

This might be more appropriate for theoretical CS stackexchange, but it feels sufficiently low level to be relevant here. Consider the following thought experiment: I have a Quantum FPGA, it is a ...
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1answer
15 views

Working out the speed of a object by its frequency and a superposition wave?

Say you have 2 loudspeakers facing each other and they are separated by 20m, but are connected to the same oscillator and so both have a signal frequency of 800Hz. I calculated the separation of the ...
2
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2answers
72 views

How can 2 EM waves null each other at a point but continue to propagate?

how can 2 EM waves (travelling in opposite directions) null each other at a point in space but continue to propagate beyond the point in space where they interact to null each other?
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3answers
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Why do travelling waves continue after amplitude sum = 0?

My professor asked an interesting question at the end of the last class, but I can't figure out the answer. The question is this (recalled from memory): There are two travelling wave pulses moving in ...
2
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1answer
103 views

Difference between phase space and Hilbert space? [closed]

Why is the phase space of classical mechanics not a vector space, but Hilbert space of QM is?
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4answers
199 views

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 ...
4
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1answer
96 views

When does the principle of superposition apply?

I assumed from my general physics courses that the principle of superposition was just an empirical fact about forces. Then I could understand that derived quantities like the $E$ and $B$ fields ...
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0answers
55 views

Classical wave equation - validity

I know that classical wave equation carries for spherical wave fronts. In addition, Huygens' principle states that any wave front is a superposition of many spherical wavelets, so why does the ...
2
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2answers
95 views

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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1answer
65 views

Why superposition is useful just for linear functions?

I saw a problem which said that we have a bar between two walls and we increase the temperature. and as you know walls push a force to the bar so the length of it does not change. in the solution I ...
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1answer
111 views

Relationship between Quantum superposition and Uncertainty principle

I'm an amateur in quantum mechanics. I am confused after reading the following in the wikipedia article about quantum superposition: If the operators corresponding to two observables do not ...
0
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1answer
53 views

Using superposition to find current

I'm given the following problem I'm a little bit confused about superposition problems when current flows through a voltage source but not the resistor. 1) When I looked at the solution for this ...
1
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1answer
77 views

Understanding amplitude amplification in quantum computing

In short, what is the essence of amplitude amplification type of techniques that appear in quantum computing? More precisely, my main questions are, relating them more to Grover's search which ...
0
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3answers
69 views

Is the sum of two stationary states of different energies also a stationary state?

The question title kind of speaks for itself really. I was thinking of maybe using the orthogonality relation to try to show this: $$\int_{-\infty}^{\infty}\phi_n(x)\phi_m(x)dx=\delta_{nm}.$$ ...
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1answer
39 views

How do we acquire c-coefficients (“weights”, “probabilities”), when dealing with superposition of stationary states? [closed]

I searched quite a lot textbooks to answer this question, but I couldn't find anything satisfactory. This could be more general question, but it will be easier to just restrain to particle (say ...
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1answer
117 views

Why is particle superposition still part of quantum mechanics? [duplicate]

After reading an article on Schrodinger's Cat, it seems that if we take the environment as an observer, that superposition cannot occur because all atomic and subatomic entities would be observed all ...
2
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1answer
92 views

Why do we hear the square of the wave?

Assume we superpose two waves of frequencies $\omega_1, \omega_2$. Then what we get are beats. Adding the two sines gives us $$\psi = A\sin(\omega_1 t) + A\sin(\omega_2 t) = 2 \sin \left(\frac{\...
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1answer
40 views

Re-entering superposition

I've realized that I'm somewhat familiar with what happens when an system in a superposition is "measured". But not at all with what happens after. Example: If there is an electron in a superposition,...
2
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1answer
100 views

How to calculate the frequency of oscillation of superposition states [closed]

Been working on this question for a while and I'm not sure how to go about it. Could someone point me in the right direction, particularly for the frequency question. The question is as follows: A ...