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Tagged with coherent-states wavefunction
6
questions
2
votes
3
answers
245
views
Finding the wavefunction of coherent state in 2D oscillator
Suppose I have a two-dimensional harmonic oscillator, $H= \hbar\omega(a_x^{\dagger}a_x+a_y^{\dagger}a_y)$. We define the operator $b=\frac{1}{\sqrt{2}}(a_x+ia_y)$.
If eigenkets of the hamiltonian are $...
- 81
0
votes
1
answer
97
views
Coherent states - scalar product [closed]
$\newcommand\norm[1]{\lVert#1\rVert}$
$\newcommand\ket[1]{|#1\rangle}$
$\newcommand\mean[1]{\langle #1\rangle}$
$\newcommand\braket[2]{\langle #1|#2\rangle}$
$\newcommand\ketbra[2]{|#1\rangle\langle #...
- 127
0
votes
1
answer
104
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Uniqueness of most classical state in quantum mechanics
Due to Heisenberg uncertainty relation $$(\Delta x)(\Delta p) \geq \frac{\hbar}{2}$$ there exist an uncertainty in measurement of displacement and momentum. The state reach minimum uncertainty $$(\...
- 567
3
votes
2
answers
109
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Normalisation in Harmonic Oscillators
For a harmonic oscillator, I can write
$$
|\alpha \rangle = e^{-\frac{1}{2}|\alpha|^2} \Sigma_n \frac{\alpha^n}{\sqrt{n!}}|n\rangle = \sum_n\langle n|\alpha\rangle|n\rangle
$$
I can also write:
$$
|x \...
- 45
5
votes
3
answers
5k
views
What is the position wavefunction of coherent states?
Consider a coherent state $|\alpha\rangle$, $\alpha\in\mathbb C$. In the context of a quantum harmonic oscillator, this is defined as the eigenvector of the annihilation operator $a$: $a|\alpha\rangle=...
- 14.8k
2
votes
1
answer
1k
views
Can the Wigner function be described using coherent states?
The Wigner function for a wave function $\Psi(\vec{r})$ is
$$
W(\vec{r},\vec{k}) = \frac{1}{2\pi} \int dy e^{-i \vec{k} \cdot \vec{y}} \Psi^{*}(\vec{r}-\vec{y}/2) \Psi(\vec{r}+\vec{y}/2) . \tag{1}
$$
...
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