All Questions
Tagged with coherent-states harmonic-oscillator
34
questions
1
vote
2
answers
66
views
Coherent creation operator: unitary or not?
In Quantum Mechanics, for coherent states $|z\rangle$ it can be prooved that if $|0\rangle$ is the vacuum state for an harmonic oscillator, therefore:
\begin{equation}
|z\rangle=e^{za^{\dagger}-z^*a}|...
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
1
vote
3
answers
242
views
It seems that expectation value of $H$ on coherent states is independent of time? But why?
Let's say the particle is in the state $| \psi(0) \rangle = \exp(-i\alpha p/\hbar) |0 \rangle$, where $p$ is the momentum operator.
I have to show that $| \psi(0) \rangle$ is a coherent state and to ...
- 81
0
votes
0
answers
69
views
Is there any way to write eigenstates of infinite square well in terms of eigenstates of harmonic oscillator?
I wanted to find Husimi Q function using expression $Q= \langle \alpha|\rho|\alpha \rangle$, where $|\alpha \rangle $ is coherent states of harmonic oscillator. I want to consider system $\rho=|u_n\...
- 781
1
vote
0
answers
117
views
Finding an operator in terms of creation and annihilation operators that satisfy some conditions
I have a problem where I'm looking to find the following Hermitian operator $\hat{A}$ written in terms of the operators $\hat{a}^{\dagger}\hat{a}$, $\hat{a}^2$, $\hat{a}^{\dagger 2}$, $\hat{a}$, $\hat{...
- 21
0
votes
0
answers
68
views
Coherent States and Temperature for Scalar QFT with Source
This is a follow-up question on a question I previously asked, namely Coherent states and thermal properties. The authors of the article I am referring to in the previous question (Thermodynamics of ...
- 3,992
0
votes
0
answers
141
views
Evolution of Quantum Harmonic Oscillator into coherent state
Why does a quantum harmonic oscillator that is driven by an electromagnetic wave in cosine form with its frequency equal to the resonance frequency of the oscillator evolve from its groundstate into a ...
- 95
0
votes
1
answer
721
views
Coherent state basis
I'm learning about coherent states in a more in depth lesson the the quantum harmonic oscillator. Coherent states are eigenstates of the lowering operator. In my head this is just saying: since any ...
- 719
2
votes
2
answers
1k
views
Driven Quantum Harmonic Oscillator
Consider the Hamiltonian
$$
H = \frac{p^2}{2} + \frac{ x^2}{2} - F(t) x.
$$
This is essentially a time dependent shifted harmonic oscillator, which can be represented as
$$
H' = \frac{p^2}{2} + \frac{...
- 427
2
votes
0
answers
57
views
Could one call eigenstates of $ \hat{a} = \hat{x} + i\hat{p}$ coherent states for other potentials than the harmonic oscillator?
Let's say I look at the quantum system of a particle in one dimension, subject to any other potential than the one of the harmonic oscillator, and I define $\hat{a}$ as stated above. I would find the ...
- 6,763
2
votes
0
answers
386
views
Quantum Harmonic Oscillator density matrix in coherent states base [closed]
I was trying to calculate matrix elements of the density operator for a 1D QHO (with Hamiltonian $\mathcal H = \hbar\omega a^\dagger a $) in the base of coherent states $\{\vert\alpha\rangle\}$ and ...
- 21
1
vote
0
answers
150
views
What is the meaning of the time evolution of a product of coherent states of the QHO?
I am trying to analyze the dynamics of a coupled quantum harmonic oscillator (cQHO) system. The Hamiltonian of the system is given by:
\begin{equation}
\hat{H}_{Coupled}=\frac{1}{2m}\sum_{j}\hat{p}_{j}...
- 325
6
votes
2
answers
731
views
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 ...
- 785
1
vote
1
answer
172
views
Probability Distribution of a Coherent Harmonic Oscillator
I'm currently reading Quantum Optics by Scully and Zubairy and come across a derivation in which I am stuck as to what to do next.
Starting with a general solution to the harmonic oscillator ...
- 268
2
votes
1
answer
998
views
Time evolution of a coherent state
$\newcommand\norm[1]{\lVert#1\rVert}$
$\newcommand\ket[1]{|#1\rangle}$
I consider an Hamiltonian of the Harmonic Oscillator $\hat{H} = \frac{P^2}{2m}+\frac{1}{2}m\omega^2 X^2$.
I proved already if the ...
- 127