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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Linearity of quantum mechanics and nonlinearity of macroscopic physics

We live in a world where almost all macroscopic physical phenomena are non-linear, while the description of microscopic phenomena is based on quantum mechanics which is linear by definition. What are ...
25
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7answers
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How is quantum superposition different from mixed state?

According to Wikipedia, if a system has $50\%$ chance to be in state $\left|\psi_1\right>$ and $50\%$ to be in state $\left|\psi_2\right>$, then this is a mixed state. Now consider state $\left|...
8
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4answers
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Why is the Principle of Superposition true in EM? Does it hold more generally?

In the theory of electromagnetism (EM), why is the principle of superposition true? Can we read it off from Maxwell's equations directly? Does it have any limit of applicability or is it a ...
7
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1answer
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Differences between pure/mixed/entangled/separable/superposed states

I am currently trying to establish a clear picture of pure/mixed/entangled/separable/superposed states. In the following I will always assume a basis of $|1\rangle$ and $|0\rangle$ for my quantum ...
11
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2answers
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Why do neutrinos propagate in a mass eigenstate?

I am aware that flavor $\neq$ mass eigenstate, which is how mixing happens, but whenever someone talks about neutrino oscillations they tend to state without motivation that when neutrinos are ...
7
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3answers
354 views

Is it possible that we have a physical state which is a mixture of discrete eigenstates and continuous ones?

For a system has both continuous and discrete spectrum, is it possible that a physical states is something like: $$\psi(x)=\sum_{n=n_1}^{n=n2}c_n\psi_n(x)+\int_{E_0-\Delta_E}^{E_0+\Delta_E}\psi_E(x)\...
65
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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 ...
10
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5answers
1k views

Plants and quantum mechanics!

I have been working on quantum biology and found something interesting that I would like to write an equation for. Scientists have wondered how plants have such a high efficiency in photosynthesis; ...
11
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3answers
422 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 - ...
6
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1answer
129 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 ...
2
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2answers
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Is Schrödinger’s cat misleading? And what would happen if Planck constant is bigger?

Schrödinger’s cat, the thought experiment, makes it seem like as if measurement can cause a system to stop being in a superposition of states and become either one of the states (collapsed). So does ...
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2answers
218 views

Quantum Eraser thought experiment with light photons of distinct color

I tried to recreate the Quantum Eraser experiment into a thought experiment with a few changes. It left me a little perplexed as to what outcomes I should expect. Any help would be appreciated. Lets ...
4
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3answers
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Classical vs qubits: Superposition

Since a quantum information lecture today I have been wondering what does it really mean for a state to be in superposition? Is this something that is answerable? This is what we learnt (or what I ...
1
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2answers
211 views

Why does the superposition principle work in method of images?

Okay, let there be a conducting sphere having radius $a$ initially charged with $Q$ & insulated. Now, $q$ is brought in front of the conductor at $y$ from the center. Now, Jackson in his book ...
0
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2answers
2k views

Can Quantum Entanglement and Quantum Superposition be considered the same phenomenon?

Quantum entanglement is known to be the exchange of quantum information between two particles at a distance, while quantum superposition is known to be the uncertainty of a particle (or particles) ...
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3answers
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How is a bound state defined in quantum mechanics?

How is a bound state defined in quantum mechanics for states which are not eigenstates of the Hamiltonian i.e. which do not have definite energies? Can a superposition state like $$\psi(x,t)=\frac{1}{\...
3
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3answers
696 views

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 ...
4
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1answer
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What exactly does Aaron D. O'Connell's experiment show?

I watched a TED talk by the scientist Aaron D. O'Connell about actually seeing quantum superposition. The link to the talk is :- http://www.ted.com/talks/...
2
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4answers
686 views

The meaning of Superposition

Is superposition purely conceptual or does it represent some real "thing"? Said another way, is superposition thought to have some tangible physical manifestation or is it simply the lack of physical ...
6
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4answers
603 views

Is a photon always in a state of superposition while traveling through space?

In the double-slit experiment, we emit a photon that is in a state of superposition (wave form) which travels through both slits to interfere with itself. When we measure which slit it went through, ...
4
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2answers
268 views

What is the physical reason behind linearity of Schrodinger's equation?

What is the physical reason for Schrodinger equation to be linear? Though in physics many interactions or dynamics are found non linear.
2
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4answers
483 views

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 ...
1
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2answers
419 views

Intuitive explanation of the waves superposition

When the two waves collide, why do they pass right through each other? Mathematically it's due to the principle of superposition: the sum of the two solutions of a wave equation is also a solution. ...
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1answer
67 views

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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4answers
194 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 ...
0
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1answer
190 views

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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2answers
215 views

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 ...
3
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4answers
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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 ...
2
votes
3answers
137 views

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 ...
2
votes
2answers
7k views

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 ...
2
votes
1answer
5k views

Deriving group velocity

At the introduction to quantum mechanic phase $v_p$ and group $v_g$ velocities are often presented. I know how to derive $v_p$ and get equation: $$ \scriptsize v_p=\frac{\omega}{k} $$ What i dont ...
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4answers
1k views

Do multiple electrons exist during superposition?

Wikipedia says: Quantum superposition is a fundamental principle of quantum mechanics that holds that a physical system—such as an electron—exists partly in all its particular, theoretically ...
1
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1answer
62 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 ...
0
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2answers
75 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 ...
0
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1answer
91 views

Current quantum theory of interference

I have always thought that the quantum theory states that interference occurs when photons behave like waves and two or more possible paths exist. Interference can then be destroyed if the path of the ...
0
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4answers
3k views

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 ...
0
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3answers
441 views

Is the superposition of stationary states a stationary state? If not, then why not?

I am a beginner in Quantum mechanics and as I understand,the superposition of stationary states is also a solution of time-independent Schrödinger equation (TISE). The wave functions that are the ...