Questions tagged [hamiltonian]
The central term in the hamiltonian formalism. Can be interpreted as an energy input, or "true" energy.
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Is many-electron system's energy bounded from above?
A many-electron system with molecular Hamiltonian under the Born-Oppenheimer approximation has a finite ground state energy, which means its eigenenergy is bounded from below.
In my research, I need ...
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Perturbation theory: Why is the inner product expressed as $\langle\psi_m^0|H'|\psi_n^0\rangle=-2V_0(-1)^{\frac{m+1}{2}}$? [closed]
Introducing a perturbation to an unperturbed state, say $\psi_n^0$, with eigenenergy $E_n^0$ yields the first degenerate state as:
$$\psi_n^1=\sum_{m\neq n}\frac{\langle\psi_m^0|H'|\psi_n^0\rangle}{(...
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Determining the Hermitian operator in a Foldy-Wouthuysen transformation
I am following the mathematical steps of a paper and at some point the authors consider a transformed Hamiltonian of the form
$$
\mathcal{H}' = e^{iS} \mathcal{H} e^{-iS}.
$$
They then follow a ...
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Non-symplectic Hamiltonian systems
I'm wondering when the phase space of a Hamiltonian system looses its symplectic structure.
I think it happens when the Hamiltonian $H$ depends on a set of other variables $S_1,...,S_k$ as well as on ...
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Details in the derivation of the Lippmann-Schwinger equation
So the argument goes that for a slightly perturbed Hamiltonian
$$
H = H_0 + V,
$$
there will be some exactly known states, $\left|\phi\right>$, solving
$$
H_0\left|\phi\right> = E\left|\phi\...
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Expectation values of fermionic operators
I'm trying to compute the matrix elements of an Hamiltonian expressed in terms of fermionic operators. The system is an Agassi model, N interacting fermions on 2 levels separated by energy $\epsilon$, ...
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Question on derivation of Schrödinger's equation [closed]
I have recently started reading Nanoscale Physics for Materials Science by Tsurumi et al. and the authors present a unique derivation of Schrödinger's equation in the first chapter:
I was wondering ...
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Energy Operator, Hamiltonian, Energy Eigenvalues [duplicate]
Can we use the energy operator $i\hbar\frac{\partial}{\partial t}$ instead of the Hamiltonian to obtain the energy eigenvalues?
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Equations of motion and infinitesimal canonical transformations
Currently, I'm diving into infinitesimal canonical transformations, with a particular focus on using the infinitesimal change $\epsilon=\delta t$ and $H$ as our generating function. So, in this ...
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