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The central term in the hamiltonian formalism. Can be interpreted as an energy input, or "true" energy.
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Obtaining Eigenvalue Expression
Say we have an excitonic system with a creation operator operator:
$$ |\Psi_{ex}\rangle=\sum_{\vec{k}} \phi(\vec{k})c^\dagger_{\vec{k}+\vec{Q}}b_{\vec{k}}|GS\rangle$$
And the Hamiltonian of the system …
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How to evaluate interaction term in Hamiltonian?
If one has an interaction term in the Hamiltonian of a system as follows:$$
\sum_{\vec{q}}V(\vec{q}) \psi(\vec{k}-\vec{q})
$$
where $\psi(\vec{k}-\vec{q})$ and $V(\vec{q})$ is the wave function and interaction …
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answer
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$\mathbf k\cdot\mathbf p$ Hamiltonian
I am looking into the $k\cdot p$ Hamiltonian approach to describe a semiconductor system. … This Hamiltonian can be diagonalized to give eigenvalues and eigenfunctions of the above Hamiltonian. …