# Tag Info

### What experimental proof of quantum superposition do we have?

"Being in superposition" is not an objective property of a quantum mechanical state. Quantum mechanical states live in a Hilbert space, where, since it is a vector space, every state can be ...

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### If quantum fields are operator valued distributions, why aren't they always smeared?

Yes, if we are mathematically careful about the distributional nature of a quantum field, then we should indeed consistently write quantum fields only as "smeared functions" $\phi(f)$. But ...

### What experimental proof of quantum superposition do we have?

The answers to your questions are immediate consequences of the definition of a quantum state. Every quantum state is a superposition for the same reason that every integer is a sum of other integers....

### Why is the usage of just linear, unitary operator that isn't necessarily self-adjoint in the middle of a bra-ket a problem?

The point is that the notation is ambiguous. Interpreted as $\langle \beta \lvert A \rvert \alpha \rangle = \langle \beta , A \alpha \rangle$ (where on the right I have reverted to the unambiguous ...
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### About sending time to infinity in a slightly imaginary direction in QFT

TL;DR: In the Gell-Mann and Low theorem the $i\epsilon$ prescription in the complex time plane is equivalent to an adiabatic cutoff of interactions. Both serve as a regularization. In more details: We ...
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### Trouble understanding Dirac's notation in "The principles of quantum mechanics"

The notation’s purpose is to accommodate for degeneracy. To construct an orthonormal basis, the eigenvalues of the operator are not enough to distinguish the eigenvectors. You need to add some ...

### Is there an identity for $\hat{a}^+ \cdot \hat{a}^+$?

No! Note that $a^{\dagger 2}$ is simply the creation operator applied twice. It does not simplify to a unique identity like the commutation relation or like writing $a a^{\dagger}$ as a function of ...
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### Problem with understanding the concept of vacuum state of a quantum field

An electric field with a value different than zero in some region of space can be considered as a coherent state of photons Coherent state vs. classical world. This is not the vacuum state. We can ...
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### Inner product not invariant in QM?

The inner product is invariant, and your contradiction comes from an incorrect method of finding bra component vectors the fact that the inner product does not correspond to multiplication of ...

### What experimental proof of quantum superposition do we have?

Wave Nature As many have pointed out, the double-slit experiment is perhaps the canonical demonstration of superposition and a macroscopically visible demonstration of quantum mechanics. But the ...

1 vote
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### Projection operator onto support of distinct observables

This is an answer to the comment. Let $H_1$ and $H_2$ be two closed subspaces of a Hilbert space. Let $H_{1,2} = H_1 + H_2$ be the closure of the algebraic sum of the subspaces. (Note: In finite ...
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### What experimental proof of quantum superposition do we have?

Now the question: Has it been somehow proven that a physical entity can a some point in time and space have a dual state (independently of the model)? Science doesn't prove statements. Scientists ...
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### What experimental proof of quantum superposition do we have?

is it only that quantum mechanics is the only known model that allows us to explain things we otherwise couldn't? Here are two examples from my side. (1) Quantum dots produce entangled photons in ...
1 vote

### Inner product not invariant in QM?

You said-"This means that any arbitrarily chosen set of basis vectors is guaranteed to be orthonormal!".... It isn't correct, you can have basis vectors which are non orthogonal for instance....
1 vote
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### What does a beam splitter look like in path-encoded notation for at most one photon?

To leave the vacuum unchanged, you need to put a $\sqrt{2}$ in the top left corner.

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