All Questions
Tagged with adiabatic schroedinger-equation
8
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165
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Finite-time effects in Landau Zener
Consider a two level system with a Landau-Zener Hamiltonian of the form
$$\hat{H}=\begin{pmatrix}v t&\beta\\\beta&-v t\end{pmatrix}.$$
The Landau-Zener formula provides a closed form for the ...
- 503
1
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1
answer
64
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Derivative of $c(t)$ in Adiabatic Approximation
In Sakurai's Modern Quantum Mechanics, second edition, $5.6.10$ is
$$\begin{aligned}
\dot{c}_m(t)=-\sum_nc_n(t)e^{i[\theta_n(t)-\theta_m(t)]}\langle m;t|\left[\frac\partial{\partial t}|n;t\rangle\...
- 37
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Adiabatic theorem for stochastic time-dependence
I am trying to derive the adiabatic theorem when my time-dependent Hamiltonian is stochastic and I have a few questions. Usually, one starts with the Schrödinger equation
\begin{equation}
i\frac{d |\...
- 87
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2
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On Adiabatic approximation
In Sakruari's Modern Physics, it's written that
$$H(t)|n;t\rangle =E_n(t)|n;t\rangle
$$
simply noting that at any particular time $t$, the states, and eigenvalues may change. If we now look for ...
- 11.9k
3
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2
answers
284
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Adiabatic Approximation, Solving the Schrödinger equation
In the adiabatic approximation one looks at the Hamiltonian
$$ H_0 = \sum_{i = 1}^{N_e} \frac{\vec{p}_i^2}{2m_e} + \sum_{i < j} \frac{e^2}{|\vec{r}_i - \vec{r}_j|} + \sum_{k < l} \frac{Z_k ...
- 324
1
vote
2
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983
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Queries of proof of adiabatic theorem in QM
I have a few questions regarding the proof of the adiabatic theorem in the book "Introduction to Quantum Mechanics" by Griffiths:
The assumptions are that if the Hamiltonian changes with time then ...
- 1,023
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Are there any specific examples of the application of Lewis-Riesenfeld procedure to time dependent Hamiltonians in QM?
Lewis-Riesenfeld invariant theory is a theory applicable to solve time-dependent Schrodinger equations. I have always encountered the theory related to the procedure, however never encountered any ...
- 595
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1
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Infinite quantum well width $L$ to $2L$ adiabatic process
If we change width of the infinite quantum well $L$ to $2L$ slowly enough, how it does change energy levels.
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