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16
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5answers
1k views

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 ...
15
votes
4answers
727 views

Why do electrons in an atom occupy only the stationary states?

When we talk about the elementary problems in quantum mechanics like particle in a box, we first calculate the energy eigen-function. Then we say that the most general state is the linear combination ...
11
votes
4answers
1k views

Schrödinger's cat; why was it necessary?

Could someone please explain to me the idea that Schrödinger was trying to illustrate by the cat in his box? I understand that he was trying to introduce the notion of the cat being both alive and ...
10
votes
3answers
2k views

What's the difference between an entangled state, a superposed state and a cat state?

1) Can a state be entangled without also being a superposition? (Please give an example.) 2) Can a state be a superposition without being entangled? (Again, an example please.) 3) And what about ...
9
votes
3answers
625 views

If superposition is possible in QM, why do we often assume systems are already in their eigenstates?

My understanding is that an arbitrary quantum-mechanical wavefunction can be written as a linear combination of eigenfunctions of some Hermitian operator, most commonly the Hamiltonian; when a ...
8
votes
2answers
611 views

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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4answers
2k views

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 ...
6
votes
6answers
2k views

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 ...
5
votes
1answer
144 views

Does the Strong Nuclear Force follow Superposition?

I have just started the study of nuclear physics in my high school, and while reading about nuclear forces and binding energy per nucleon, I found out that the nuclear forces are highly short ranged ...
5
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1answer
2k views

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 ...
4
votes
3answers
471 views

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 ...
4
votes
2answers
165 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.
4
votes
1answer
500 views

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 :- ...
4
votes
1answer
160 views

Experimental relationship between linear dependence and superposition

From Griffith's Introduction to Electrodynamics The principle of superposition may seem obvious to you, but it did not have to be so simple: if the electromagnetic force were proportional to the ...
4
votes
2answers
76 views

Should the eigenkets be weighted in $|P\rangle = \sum\limits_{r}|\xi^r\rangle$?

Page 37 of Dirac's book The Principles of Quantum Mechanics, states The condition for the eigenstates of $\xi$ to form a complete set must thus be formulated, that any ket $|P\rangle$ can be ...
3
votes
3answers
260 views

Why are the energy eigenstates realized in atomic transitions?

I have a question like "Why is it often assumed that particles are found in energy eigenstates?", it is a little different, though. When one solves the hydrogen atom, one can use a polynomial Ansatz ...
3
votes
1answer
245 views

Bra-ket notation, Bits, & Superposition

I am a quantum computing enthusiast, and recently I stumbled upon this the following two propositions: $$ \alpha|1\rangle + \beta|0\rangle$$ What does this mean? My understanding of this is that: ...
3
votes
4answers
339 views

Is this statement about quantum mechanics valid?

In Philosophy of Language by William G. Lycan, there are the lines: Even apparent truths of logic, such as truths of the form "Either P or not P", might be abandoned in light of suitably weird ...
3
votes
2answers
360 views

Linearity of Quantum Mechanics?

The proof of the No-Cloning Theorem states "By the linearity of quantum mechanics, ..." -- Could someone please give me a rough sketch/outline of what this means? Does it have to do with the Hilbert ...
3
votes
2answers
68 views

Can I alternate between notes really fast and have it sound like a chord?

The question basically amounts to whether I can construct the illusion of superposition with adjacent sine waves of varying frequency. Context I'm trying to play music on a Tesla Coil (like OneTesla ...
3
votes
4answers
589 views

Why is quantum entanglement so important?

Entanglement also allows multiple states to be acted on simultaneously, unlike classical bits that can only have one value at a time. Entanglement is a necessary ingredient of any quantum ...
3
votes
4answers
548 views

Is the superposition principle universal?

In David J. Griffiths' Introduction to Electrodynamics, he claims that the superposition principle is not obvious but has always been found to be consistent with the experiments. So I was wondering ...
3
votes
3answers
390 views

How can we create superposition in QM?

How can we force a particle (let's say that we know this particle has spin up) to be in a superposition of spin up and down? Wouldn't literally any interaction of it with anything cause it to be in ...
3
votes
3answers
1k views

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 ...
3
votes
1answer
161 views

Schrödinger's cat and the difficulty of macroscopic superposition state

The Schrödinger's cat was regarded as peculiar since we seldom encounter a superposition state in macroscopic scale: $$ | \mathrm{dead \,\,cat} \rangle + | \mathrm{alive \,\, cat}\rangle $$ We more ...
3
votes
1answer
139 views

Superpositions with two observers

This is a bit of an odd question. I'm not a physicist, so bear with me if I say something wrong. Lets say you have some sort of quantum event where matter is in a superposition. Standing next to you ...
3
votes
2answers
171 views

What happens when you pass a current through a coil made of a ferromagnetic substance?

I know when you pass a current through a length of copper coil or a solenoid, there is the induction of a magnetic flux. But what of the coil made of the ferromagnetic material, the permanent type ...
3
votes
0answers
92 views

Superposition principle and polarization

I am reading an optics book (Physics of Light and Optics by Peatross and Ware) that asserts this: A beam of light can always be considered as an intensity sum of completely unpolarized light and ...
2
votes
3answers
296 views

Plants and Quantum Mechanics!

So, 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 ...
2
votes
4answers
262 views

Nonlinear waves superposition

Non-linear waves do not superimpose to each other, but why? What characteristics give this property?
2
votes
2answers
82 views

Is superposition principle equally valid for both scalar and vector quantities?

I was wondering if superposition is even applicable to scalar quantities because scalars should simply add up to give final result as there is no sense of direction. Do we have any example of a vector ...
2
votes
4answers
556 views

Does measuring destroy entanglement

Before measuring a quantum particle(photon) it exists in a superposition state, once we observe(measure) it, it settles in one of the possible states(destroying superposition). For entangled ...
2
votes
2answers
139 views

Undamped oscillations. Why is the solution a linear combination of $\sin()$ and $\cos()$?

$ma = mg - cx$, where $x(0) = x_0 = 0$ is the position in which there is no tension in the rope. $dx/dt = v_0$ for $t = 0$; $v_0$ is a known constant. The discriminant of the characteristic ...
2
votes
1answer
563 views

How do we know superposition exists?

How do we know superposition exists? Has it been observed, or has it been deduced, and how certain are we? The Copenhagen Interpretation seems to imply that superposition collapses into one state ...
2
votes
2answers
74 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: ...
2
votes
2answers
3k 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
2answers
55 views

Where the extra power comes from?

Suppose we have two radio waveforms each has amplitude of 1, then the total power is 2. Suppose these two waveforms add up some where constructively, then the amplitude become 2, and the total power ...
2
votes
2answers
217 views

What does the Copenhagen interpretation say about the position of a particle before measurement?

Suppose there is a particle in space. When we measure the position of that particle, we get a particular value with a probability that can be calculated from the wave function. But, according to the ...
2
votes
2answers
1k views

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 ...
2
votes
1answer
56 views

Calculating probability of finding the particle using Dirac notation

An electron can be in one of two potential wells that are so close that it can ‘tunnel’ from one to the other. Its state vector can be written $|ψ\rangle = a|A\rangle + b|B\rangle$, where ...
2
votes
1answer
102 views

What is a virtual state?

In quantum mechanics / Raman spectroscopy, what is a virtual state? What is the difference between a virtual state and a superposition of states? Can you simply think of the virtual state as a ...
2
votes
2answers
55 views

Could there be a correlation between the earth's magnetic field and quantum superposition

I do apologise in advance for what might seem like a stupid question coming from a non-physicist. But I was wondering if the earth’s magnetic field could influence the wave pattern that one observes ...
2
votes
1answer
149 views

Principle of Superposition for driven oscillator

So I understand the the Superposition Principle states that all the forced oscillations, as determined by multiple external forces, are to be added up in order to get the entire solution. However, ...
2
votes
2answers
151 views

When do we see particles to be in a superposition of energy states?

I have two doubts: Exactly when does this happen? and If we are in a superposition of states (lets say E1 and E2) and the particle absorbs a photon, what will happen? If E3-E1 = hf, will it go to E3? ...
2
votes
1answer
122 views

Normalization of a wavefunction that's superposition of two unknown energy eigenfunctions

Question:$$\psi(x)=A(3u_1(x)+4u_2(x))$$where $u_1(x)$ and $u_2(x)$ are energy eigenfunctions. How to normalize function $\psi(x)$? My intuitive solution: I got ...
2
votes
2answers
54 views

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 ...
2
votes
0answers
58 views

Proton as superposition of hadrons: $\vert p\rangle = c_0\vert p_0\rangle+c_1\vert h\rangle+\cdots$

I have a question regarding hadron fluctuations. For instance on page 85 in Feynman's "Photon-Hadron Interactions" equation 15.2 reads: $$\tag1\vert \omega\rangle = \vert ...
2
votes
1answer
159 views

Can you tell if a particle is in superposition?

This may be an easy answer for anybody. Is it possible to detect if a particle A is still in a superposition via the sending a group of particles B through a box containing particle A?
1
vote
3answers
68 views

Superposition principle

If $S=(v_{1},v_{2}......v_{n})$ is a basis for vector Space V, then every vector v in V can be expressed in the form of $v=c_{1}v_{1}+.......c_{n}v_{n}$ in an unique way. Explain the significance of ...
1
vote
2answers
92 views

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?