All Questions
Tagged with adiabatic approximations
17
questions
3
votes
1
answer
104
views
Adiabatic Approximation in the spin 1/2 System
I am studying the following Hamiltonian:
$$H(t) = \begin{bmatrix}
\frac{t\alpha}{2} & H_{12} \\
H_{12}^* & -\frac{t\alpha}{2} \\
\end{bmatrix}$$
I want to assume that $\...
1
vote
1
answer
64
views
Derivative of $c(t)$ in Adiabatic Approximation
In Sakurai's Modern Quantum Mechanics, second edition, $5.6.10$ is
$$\begin{aligned}
\dot{c}_m(t)=-\sum_nc_n(t)e^{i[\theta_n(t)-\theta_m(t)]}\langle m;t|\left[\frac\partial{\partial t}|n;t\rangle\...
- 37
3
votes
0
answers
41
views
What is the relation between the Adiabatic Approximation used in quantum chemistry and the one given in QM textbooks?
I am an aspiring quantum chemist and have come across two vastly different versions of the Adiabatic Approximation when studying Quantum Mechanics from the perspective of physics and chemistry ...
- 89
0
votes
1
answer
67
views
Why can't we use the time-dependent Schrödinger equation twice in the adiabatic approximation derivation?
In the standard derivation of the adiabatic approximation (see Sakurai in Modern Quantum Mechanics, Wikipedia) a differential equation for the coefficients is reached as
$$
i\hbar \dot{c}_m(t) + i\...
- 602
0
votes
2
answers
105
views
In the adiabatic theorem, how do we know which eigenstate we start on? (STIRAP)
I am aware of the question here, but it doesn't have an answer and also doesn't answer my question. I'm wondering about a specific case in STIRAP, where the 3 eigenstates are $$|\Psi_\pm\rangle = \...
- 700
1
vote
1
answer
67
views
"Classical" adiabatic approximation: please help me understand better
In this1 paper they use an adiabatic approximation to reduce two differential equations to one. Could you please recommend some alternative reading for this (semi) classical adiabatic approximation, ...
- 962
0
votes
2
answers
66
views
On Adiabatic approximation
In Sakruari's Modern Physics, it's written that
$$H(t)|n;t\rangle =E_n(t)|n;t\rangle
$$
simply noting that at any particular time $t$, the states, and eigenvalues may change. If we now look for ...
- 11.9k
2
votes
2
answers
401
views
Berry phase disappearing in adiabatic approximation?
The celebrated adiabatic theorem states that for a system initially in the eigenstate $|\psi(0)\rangle = |n(0)\rangle$ for $t=0$, it will stay in that state afterward under adiabatic evolution:
$$
|\...
- 169
0
votes
0
answers
659
views
Understanding the adiabatic and sudden/diabatic approximations?
I’m trying to build a stronger understanding of what the adiabatic and sudden/diabatic approximations mean and imply through examples. Specifically, I want to know how energy is transferred based on ...
- 419
1
vote
1
answer
201
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Why can the equation of adiabatic process $P_1 V_1^\gamma=P_2 V_2^\gamma$ be written as $\Delta P/P=-\gamma \Delta V/V$?
Why can the equation of adiabatic process $P_1 V_1^\gamma=P_2 V_2^\gamma$ be written as
$$\frac{\Delta P}{P}=-\gamma \frac{\Delta V}{V},$$
where $P_2-\Delta P=P_1$ and $V_2+\Delta V=V_1$ as in ...
- 11
3
votes
0
answers
242
views
Phase-shifting of instantaneous eigenstates in the adiabatic approximation
In my book Quantum Mechanics by B.H. Bransden and C.J. Joachain, there is a chapter on the adiabatic approximation.
Here, the authors assume that the time-dependent Hamiltonian $\hat{H}(t)$ changes ...
- 131
1
vote
0
answers
248
views
Is the adiabatic theorem in Quantum mechanics valid in general for Non-Hermitian Hamiltonians?
Is the adiabatic theorem in Quantum mechanics valid in general for Non-Hermitian Hamiltonians? The proofs I have come across for adiabatic theorem all assume at some point in the proof that the ...
- 103
5
votes
2
answers
2k
views
Condition for adiabatic approximation, derivation?
In quantum mechanics it is said that an adiabatic approximation is valid when
$$T\gg \frac{\hbar}{\Delta E},$$
where $T$ is the time scale of variation of the Hamiltonian and $\Delta E$ is the typical ...
2
votes
0
answers
867
views
Adiabatic approximation and time-dependent problems
I am an undergraduate physics student. I have a question in approximation methods for time-dependent problems in quantum mechanics. I read the proof of the adiabatic theorem but I didn't understand it....
user27058
11
votes
2
answers
1k
views
When is the adiabatic approximation for solid state systems valid?
The adiabatic approximation for solid state systems is rather radical. I was wondering in which cases it breaks down.
As it is based on the idea of the nuclii being much heavier than the electrons I ...
- 1,418