Questions tagged [hamiltonian]
The central term in the hamiltonian formalism. Can be interpreted as an energy input, or "true" energy.
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Schroedinger equation applicable only in electron
I am new to quantum mechanics - I started reading a book about it one week ago- and I have a question about the Schroedinger equation.
We know that the time-dependent Schroedinger equation has the ...
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Why is the ground state important in condensed matter physics?
This might be a very trivial question, but in condensed matter or many body physics, often one is dealing with some Hamiltonian and main goal is to find, or describe the physics of, the ground state ...
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Connection between dispersion relation and symmetries of the Hamiltonian
I am having trouble understanding intuitively the connection between the dispersion relation and the symmetries of the Hamiltonian. For example, suppose we have a lattice and there are four sub-...
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Momentum space representaion of an electron-phonon coubling Hamiltonian
I am facing a problem transforming the following Hamiltonian into momentum space:
\begin{align}\hat{H} = -\gamma \sum_\alpha\sum_{i=1}^2 \hat{X}_{i,\alpha} \hat{c}_{i,\alpha}^+\hat{c}_{i,\alpha} +t\...
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Hamiltonian of a system? [closed]
I have a three level lambda system with two ground states $\lvert1\rangle$ and $\lvert3\rangle$ and an excited state $\lvert2\rangle$, interacting with a classical field and the SPP mode of the ...
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Calculating the expectation value of a spin operator in a uniform magnetic field
I'm trying
Usually for these types of questions, I'm used to the field being in a specific direction.
For example, if the field was in the $z$ direction, I could find this solution by checking
$|\...
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Relationship between unitaries generated by a Hamiltonian and its negative sign
Consider two unitary operations $U_1$ and $U_2$ defined by:
$\partial_t U_1 = -iH_1U_1$ and $\partial_t U_2 = iH_1U_2$
Here, $U_1$ is generated by $H_1$ and $U_2$ is generated by $-H_1$, with the ...
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Hamiltonian eigenvalues in a transformed reference frame
Under a time-dependent unitary transformation $V(t)$ of the state vectors $|{\psi}\rangle$
\begin{equation}
|\psi'(t)\rangle = V(t) |\psi(t)\rangle
\end{equation}
The Hamiltonian $H(t)$ has to ...
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Solving Periodic Time Dependent Hamiltonians
For a general time dependent Hamiltonian, if the Hamiltonian at two different times $t_1,\,t_2$ satisfies $$\left[ \hat{H}(t_1),\hat{H}(t_2) \right]=0,$$ then the time evolution operator is $\hat{U}(t)...
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Higher-order (e.g. $n$th-order) corrections to (non-degenerate, time-independent) perturbation theory in QM?
In perturbation theory for quantum mechanics, using Schrodinger equation and the expansions $$H=H_0+\varepsilon H_1+\varepsilon^2 H_2+\cdots$$
and $$E_n=E_n^{(0)}+\varepsilon E_n^{(1)}+\varepsilon^2 ...
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Hamilton's characteristic and principal functions and separability
Just hoping for some clarity regarding Hamilton's characteristic function $W$. When we take a time independent Hamiltonian we can separate the Principal function $S$ up into the characteristic ...
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Can one assign a Hamiltonian under a general time-dependent transformation in quantum mechanics?
The time evolution of states under a time-dependent Hamiltonian $H_S(t)$ in the Schrödinger picture is determined by
$$
\label{TDS}
i\hbar \frac{d |{\psi(t)}\rangle}{dt} = H_{\mathrm{S}}(t) |\psi(t)\...
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Time-evolution operator in QFT
I am self studying QFT on the book "A modern introduction to quantum field theory" by Maggiore and I am reading the chapter about the Dyson series (chapter 5.3).
It states the following ...
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How to get $ H=\int\widetilde{dk} \ \omega a^\dagger(\mathbf{k})a(\mathbf{k})+(\mathcal{E}_0-\Omega_0)V $ in Srednicki 3.30 equation?
We have integration is
\begin{align*}
H =-\Omega_0V+\frac12\int\widetilde{dk} \ \omega\Big(a^\dagger(\mathbf{k})a(\mathbf{k})+a(\mathbf{k})a^\dagger(\mathbf{k})\Big)\tag{3.26}
\end{align*}
where
\...
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What theorem is behind writing an operator in matrix form as outer products?
Consider a Hamiltonian of a two state system that follows, for the two eigenstates:
$$H|\phi_1\rangle = E_1|\phi_1\rangle \ ; \ H|\phi_2\rangle = E_2|\phi_2\rangle $$
Its matrix can be represented as:
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