# Questions tagged [hamiltonian]

The central term in the hamiltonian formalism. Can be interpreted as an energy input, or "true" energy.

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### Confused about AC Stark effect

Can someone explain to me in an intuitive way (or a nice mathematical demonstration) or point me towards some accessible papers about the AC Stark effect (Autler-Townes effect)? I am mainly confused ...
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### Time dependence of ladder operators in QFT

I'm currently going through Matthew D. Schwartz book Quantum Field Theory and the Standard Model, p. 23. For free (non interacting) field theories we are able to quantise the field by expanding our ...
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### Scattering, 4 point correlator, #distinct Feynman diagrams

In order to compute the scattering probability that two particles of type 1 (associated to $\phi_1(x)$) which come from the far past with the momenta $p_1$ and $p_2$, to scatter and evolve into two ...
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### Construction of propagator for time-dependent hamiltonian

In deriving a general propagator to the time-dependent ($H = H(t)$) Hamiltonian problem, Shankar works to first order in $\Delta = T/N$ (a small time interval for large $N$) and argues that by ...
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### Generator of Time Shift in Classical and Quantum Mechanics

The time evolution of a point in phase space in classical mechanics can be described as \begin{equation}\label{eq:TmeShift} ( q_i(t + \Delta t),p_i(t + \Delta t) ) = \left( 1 - i\Delta t \hat{L}\...
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### Eliminating an eigenvalue from the Hamiltonian

I have a momentum space Hamiltonian $H(\vec k)$ for a Kagome lattice and I want to find its eigenvalues which may be dependent on $\vec k$. Now, I'm told that one of the eigenvalues for such ...
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### How the Hamiltonian of a classical system expressed in quantum mechanics?

I was dealing with a problem, which said that, Supposedly Hamiltonian of a conservative system in classical mechanics is $\omega xp$, where $\omega$ is a constant, and $x$ and $p$ are the position ...
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### Is this called an operator?

Consider the Hamiltonian: $$H=D\bigg(S_z-\frac{1}{3}S(S+1)\bigg)$$ Where $S_z$ is the spin-$z$ operator (one half the Pauli matrix for a doublet state) and the matrix representation of $S$ is the unit-...
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### Utility of the Magnus expansion (preserving symplectic form?)

There are (at least) two ways to perturbatively solve a matrix initial value problem: the Dyson expansion and the Magnus expansion To be explicit, suppose you're solving for a (interaction-picture) ...
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### Why are time derivatives of states in QFT equal to zero?

In equation 6-38 on page 176 of the book "Student Friendly QFT" by Robert D. Klauber it is said that the partial derivative w.r.t. time of a multi-particle state is equal to zero since we ...
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### Identifying the relevant directions in the Ising model renormalization

I'm reading the chapter about the renormalization group in Yeoman's book "Statistical mechanics of phase transitions" and I'm puzzled about how the author relates the scaling of the RG with ...
I am reading Negele & Orland's "Quantum many-particle systems". In problem 1.9 you show that the (Bethe ansatz) wave function $$\psi(\{x \}) = \exp \left( - \alpha \sum_{i < j}^N |... 2answers 200 views ### Electronic component of the Hamiltonian operator and uncertainty principle This question has to do with the concept of uncertainty principle. The Hamiltonian operator has the electronic component that takes the inverse of the distance between any two electrons. My question ... 1answer 639 views ### Is there a physical interpretation to invariant random matrix ensembles? Disclaimer. I am a graduate student in pure mathematics, so my knowledge of physics more advanced than basic 1st/2nd year undergraduate physics is very limited. I welcome corrections on any ... 0answers 14 views ### Predictability in decoherence theory to find the classical states: at which time must we evaluate? I have read Decoherence, einselection, and the quantum origins of the classical, end a way to quantify the classicality of states is the following. We have the system S and its environment E. The ... 1answer 23 views ### T-odd vs T-violation I am a bit confused by the difference between T-odd and T-violation. For example, I read that the existence of a fundamental particle EDM is a violation of time symmetry. However, placing an ... 1answer 82 views ### How to write the time-dependent Schrödinger equation from generic functions? Given the initial state:$$\Psi(x,t=0)=c_1 \psi_1(x)+c_2\psi_2(x)+c_yy(x)$$where \psi_1 and \psi_2 are eigenstates of \hat{H} and y(x) is a normalizable function but is not eigenstate of \... 0answers 23 views ### Book about the measurement energy of the Hamiltonian I am searching for a book about the measurement energy of hamiltonian in adiabatic quantum computing. Have you ever seen good resources? I need good references for my work. 1answer 36 views ### From spins to fields In statistical field theory, one usually considers the so-called Landau Hamiltonian:$$\beta H = \int d^{d}x\bigg{[}\frac{t}{2}m^{2}(x) + \alpha m^{4}(x)+\frac{\beta}{2}(\nabla m)^{2}+\cdots+ \vec{h}\...
Let us consider a classical dynamical system whose obserbvables $A$ evolve according to the following equation of motion \begin{align} \dot A &= -\{H,A\}+f(q) \end{align} $f(q)$ is a non-...