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Quantum mechanics describes the microscopic properties of nature in a regime where classical mechanics no longer applies. It explains phenomena such as the wave-particle duality, quantization of energy, and the uncertainty principle and is generally used in single-body systems. Use the quantum-field-theory tag for the theory of many-body quantum-mechanical systems.

2 votes

What is the most general unitary that commutes with a one dimensional projector in a finite ...

As Lagerbaer pointed out, working with finite dimension can be done in matrix representation. The projector on $|0\rangle$ has only the top left element nonzero, $\hat{\Pi}_0 = \mathrm{diag}(1,0,0,\ld …
Ondřej Černotík's user avatar
1 vote
Accepted

Understanding a sagnac interferometer with the half-silvered mirror reversed

Assuming a balanced beam splitter (BS) and denoting $|k\rangle$ state corresponding to $k$ passages of the photon through the loop, the state can be found iteratively as follows: After the first pas …
Ondřej Černotík's user avatar
4 votes

Density Operator, Expectation Value, Coherent States

The calculation $\langle \hat{X}\rangle = \mathrm{Tr}(\hat{\rho}\hat{X})$ is a good way to go. Now you just need to express the operator using creation and annihilation operators, $\hat{X} = \hat{a}+\ …
Ondřej Černotík's user avatar
2 votes

One-photon-at-a-time effect on double slit experiment with detectors?

Theoretically speaking, Cristi Stoica is right. But we can also consider more realistic scenarios or different kinds of detectors. If we start with a realistic detector able of detecting single photo …
Ondřej Černotík's user avatar
6 votes

when photons can be trapped in a cavity and manipulated. How they can be observed without be...

There is a difference between wave function collapse and destroying a photon. Normally, when you detect a photon, you let it hit a device, where the photon is absorbed and its energy is transferred to …
Ondřej Černotík's user avatar
1 vote

Why are the equal probabilities for Bell state measurement outcomes essential for "quantum t...

When the probability is the same for all teleported states, the Bell state measurement does not give us any information about the teleported state. That is an important feature of the quantum teleport …
Ondřej Černotík's user avatar
8 votes
Accepted

Meaning of $\int \phi^\dagger \hat A \psi \:\mathrm dx$

I'll start with the second one. $\int\phi^\ast\psi\,\mathrm{d}x$ is, as Chris says in the comments, the scalar (or dot) product of $\phi$ and $\psi$. In the Dirac notation, it is written as $\langle\p …
Ondřej Černotík's user avatar
2 votes

Does the reduced density matrix describes a real mixed state?

When you have a system in the state $|\psi\rangle = a|01\rangle+b|10\rangle$ and take the partial trace over the subsystem B, you will find subsystem A in a mixed state as you say. When you measure th …
Ondřej Černotík's user avatar
2 votes

What is the name of the equation which led to the Schrödinger one?

This equation is known as Helmholtz equation and is widely used especially in optics.
Ondřej Černotík's user avatar
1 vote

How to understand "always create before we annihilate, not the other way around"?

As others pointed out, the statement probably means that if you want to have a nonzero contribution from creation and annihilation operators acting on vacuum, you need to apply the creation operator f …
Ondřej Černotík's user avatar
4 votes

Zero point fluctuation of an harmonic oscillator

You can find the value of zero point fluctuations just by calculating the variance $\langle(\Delta\hat{x})^2\rangle = \langle\hat{x}^2\rangle$ in the vacuum state. You can do this either using the $x$ …
Ondřej Černotík's user avatar
1 vote
Accepted

Problem in Grandfather paradox

First important thing to note is, as Peter Shor points out, that this is just a simulation. There is a model that describes, how time travel could work on the quantum mechanical level and this is just …
Ondřej Černotík's user avatar
0 votes

Using quantum entanglement to send messages back to the past

I don't know what kind of experiment might work like that. The only thing that comes to mind is that it could somehow exploit the superluminal speed of wavefunction collapse to transmit information. B …
Ondřej Černotík's user avatar
4 votes

Does measuring destroy entanglement

That depends on what kind of measurement you have in mind. Don't forget that often what is a measurement outcome from one point of view is a superposition from another. So some kind of superposition c …
Ondřej Černotík's user avatar
1 vote

Why does a damped quantum harmonic oscillator have the same decay rate as the equivalent cla...

Harmonic oscillators are—from a certain point of view—very boring quantum systems. Unless they're coupled to some nonlinear elements, their quantum evolution is exactly the same as the evolution of a …
Ondřej Černotík's user avatar

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