Questions tagged [hamiltonian]
The central term in the hamiltonian formalism. Can be interpreted as an energy input, or "true" energy.
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When is the Hamiltonian of a system not equal to its total energy?
I thought the Hamiltonian was always equal to the total energy of a system but have read that this isn't always true. Is there an example of this and does the Hamiltonian have a physical ...
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What does it mean for a Hamiltonian or system to be gapped or gapless?
I've read some papers recently that talk about gapped Hamiltonians or gapless systems, but what does it mean?
Edit: Is an XX spin chain in a magnetic field gapped? Why or why not?
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Why do excited states decay if they are eigenstates of Hamiltonian and should not change in time?
Quantum mechanics says that if a system is in an eigenstate of the Hamiltonian, then the state ket representing the system will not evolve with time. So if the electron is in, say, the first excited ...
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The formal solution of the time-dependent Schrödinger equation
Consider the time-dependent Schrödinger equation (or some equation in Schrödinger form) written down as
$$
\tag 1 i\hbar \partial_{t} \Psi ~=~ \hat{H} \Psi .
$$
Usually, one likes to write that it has ...
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State of Matrix Product States
What is a good summary of the results about the correspondence between matrix product states (MPS) or projected entangled pair states (PEPS) and the ground states of local Hamiltonians? Specifically, ...
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Is the Ground State in QM Always Unique? Why?
I've seen a few references that say that in quantum mechanics of finite degrees of freedom, there is always a unique (i.e. nondegenerate) ground state, or in other words, that there is only one state (...
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Evolution operator for time-dependent Hamiltonian
When I studied QM I'm only working with time independent Hamiltonians. In this case the unitary evolution operator has the form $$\hat{U}=e^{-\frac{i}{\hbar}Ht}$$ that follows from this equation
$$
i\...
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Detailed derivation and explanation of the AKLT Hamiltonian
I am trying to read the original paper for the AKLT model,
Rigorous results on valence-bond ground states in antiferromagnets. I Affleck, T Kennedy, RH Lieb and H Tasaki. Phys. Rev. Lett. 59, 799 (...
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Is there a physical interpretation to invariant random matrix ensembles?
Disclaimer. I am a graduate student in pure mathematics, so my knowledge of physics more advanced than basic 1st/2nd year undergraduate physics is very limited. I welcome corrections on any ...
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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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Constructing Lagrangian from the Hamiltonian
Given the Lagrangian $L$ for a system, we can construct the Hamiltonian $H$ using the definition $H=\sum\limits_{i}p_i\dot{q}_i-L$ where $p_i=\frac{\partial L}{\partial \dot{q}_i}$. Therefore, to ...
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Does the poisson bracket $\{f,g\}$ have any meaning if neither of $f$ or $g$ is the system's Hamiltonian?
Say one has a mechanical system with hamiltonian $H$, and two other arbitrary observables $f,g$. $H$ is super useful since $\{H, \cdot\} = \frac{d}{dt}$. But does $\{f,g\}$ give any useful information ...
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What is the Hamiltonian of General Relativity?
We know that reparametrization-invariance of an action leads to a Hamiltonian which is identically zero. Check Edmund Bertschinger: Symmetry Transformations, the Einstein-Hilbert Action, and Gauge ...
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How do I simulate an atom?
Let us assume I wish to simulate a Helium atom, since there does not exist a closed-form solution.
However, I presume I would need to simulate the time-dependent Schrodinger wave equation. I would ...
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Why particle hole symmetry and chiral symmetry are called symmetries?
$PHP^{-1}=-H$ (particle-hole symmetry)
and
$\Gamma H \Gamma^{-1}=-H$ (chiral symmetry)
I understand why we get the negative signs but im just a bit confused as to why such equalities mean $H$ is ...
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