Questions tagged [coherent-states]
The specific quantum state of the quantum harmonic oscillator, often described as a state which has dynamics most closely resembling the oscillatory behavior of a classical harmonic oscillator. It obeys the minimal uncertainty relation in Heisenberg's uncertainty relationship.
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Harmonic oscillator coherent state expectation values
I'm looking to calculate the expected values of a coherent state (of a harmonic oscillator) evolving in time. I know that the $x$ and $p$ expectation values are as in classical motion, but I'm ...
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Boundary conditions in holomorphic/coherent state path integral
Consider the holomorphic representation of the path integral (for a single degree of freedom):
$$ U(a^{*}, a, t'', t') = \int e^{\alpha^{*}(t'') \alpha(t'')} \exp\left\{\intop_{t'}^{t''} dt \left( -a^...
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Eigenstates of the creation operator
We know that coherent states $\vert\alpha\rangle$ are eigenvectors of the annihilation operator $\hat{a}$, i.e.
$$
\hat{a} \vert\alpha\rangle = \alpha \vert\alpha\rangle
$$
while the creation operator ...
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Where do fermionic coherent states live?
Although there have been a couple of questions on fermionic coherent states, I don't think any has answered the question "on what space do fermionic coherent states live?", or at least not ...
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Why is laser light described by a coherent state?
This is a follow-up to this recent answer by Wouter to this related question from 2015, and a comment by Emilio Pisanty underneath.
I have read the papers by Mølmer, Bartlett et al., Wiseman, and ...
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Why are coherent states of harmonic oscillators called "coherent"?
Why are coherent states of the harmonic oscillator called coherent? Coherent in what sense? Why are these states so special/useful?
From Wikipedia:
In physics, two wave sources are perfectly ...
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How to understand the completeness relation for coherent states in the "coherent space"?
In a set of notes it is stated that: Given coherent states of a harmonic oscillator $$| \alpha \rangle = \pi^{-\frac{1}{2}} \text{exp}(-\frac{1}{2}|\alpha|^2)\sum_{n = 0}^{\infty} \frac{\alpha^n}{(n!)^...
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Why use coherent state path integral? What is its motivation or goal?
In almost all textbooks of quantum field theory for high energy, they insert the position and momentum eigenstate to formulate the path integral. While in condensed matter field theory, they insert ...
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Calculating free energy from coherent state path integral
Edit: It turns out that problem encountered in this question is not limited to BdG Hamiltonians.
I am having trouble in using the coherent state path integral approach to calculate the free energy. ...
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Derivation of $P$ representation of the thermal density operator
I'm trying to derive the P representation for the thermal state
$$
\rho = \sum_{n=0}^\infty \frac{\mathrm{e}^{-\beta \omega n}}{Z} |n\rangle \langle n |
$$
where $\beta$ is the inverse temperature, $...
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Why do coherent states behave semi-classically, but harmonic oscillator states do not?
A coherent state of the quantum harmonic oscillator is defined as an eigenvector $|\alpha\rangle$ of the annihilation operator $\hat a$ with eigenvalue $\alpha$ or as spatial translations of the ...
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Coherent state vs. classical world
I am very curious as to how the classical field theory emerges from quantum field theory. In free quantum field theories, coherent states have classical properties, namely that the observables' ...
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BCS groundstate as eigenstate of the Cooper pair annihilation operator
In section 3.7 of his book Introduction to Superconductivity (2nd Ed.), Tinkham states that
[...] we note that S has the eigenvalue $e^{i\varphi}$ in a BCS state in which the the phase of $\Delta$ [.....
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Coherent states of the form $|{-\alpha}\rangle$
I've a brief question about coherent states in quantum mechanics.
As everyone knows, a coherent state is just the proper state of the anhilitation operator $a$, thus they're defined with the ...
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What is a coherent state?
In quantum mechanics, what exactly is a coherent state, and how does it differ from other states?
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