# Questions tagged [hamiltonian]

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

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### Hubbard model diagonalization in $k$-space

I am trying to diagonalize Hubbard model in real and k-space for spinless fermions. Hubbard model in real space is given as: $$H=-t\sum_{<i,j>}(c_i^\dagger c_j+h.c.)+U\sum (n_i n_j).$$ I solved ...
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### Why do we "normal-order" instead of just subtracting off vacuum energy?

The Hamiltonian is arbitrary upto a constant anyway. Why don't we just subtract off the vacuum energy? The Hamiltonian was always observable only upto a constant. Instead, we do normal-ordering, in ...
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### Why inverse flow of separable Hamiltonian with even kinetic energy can be written like this?

Why is it true that the inverse of the flow of a separable Hamiltonian with even kinetic energy can be written as $\phi_N \circ \varphi_t \circ \phi_N$ where $\varphi_t$ is the flow of the Hamiltonian ...
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### What is a symmetry of a physical system?

If I understand correctly, in many context in physics (quantum mechanics?), a physical system is specified by giving its Hamiltonian. I also hear that symmetries are rather essential. As far as the ...
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### How to find ladder operators that diagonalize a Hamiltonian in QFT?

I have some trouble understanding how one can, in the context of QFT, diagonalize a Hamiltonian $H$ by the introduction of ladder operators $a$ and $a^\dagger$ (I have trouble understanding how one is ...
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### Time-reversal symmetry for spin Hamiltonian

In the topology online course by TU Delft, the time-reversal operator acting on a system of spin-1/2 particles is introduced as $$\mathcal T = i\sigma_y\mathcal K.$$ I understand this acts on the ...
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### Why I cannot write the time evolution operator $e^{-i(T+V)t}$ as the product of operators $e^{-iTt}e^{-iVt}$

To calculate the wave equation of a time-independent Hamiltonian we use: $$\Psi_{i}(r,t)=e^{-iH^{0}t}\psi_{i}(r,0).$$ We also know that the time-independent Hamiltonian $H^{0}=T+V$ is given to the ...
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### Question on quantum field theory

I saw on Ryder's "Quantum Field Theory" book in chapter 7 where he writes down the hamiltonian of a real scalar field as \begin{equation} \begin{split} H&=\int d^3x[(1/2)(\partial_t \phi)...
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### For a quantum system with two contacts, how does one construct the contact hamiltonian for NEGF transport?

For context, I have been going through Supriyo Datta's NEGF course, slides, lecture material, and have been learning how to simulate quantum transport in his formalism. For simplicity, consider a 1D-...
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### In an $n$ particle system, why is the Hamiltonian summed over $n$?

Suppose I am working in a system consisting of $n$ particles. Thus the phase space will be $\mathbb{R}^{6n}$, and both the momentum and position space will be $\mathbb{R}^{3n}$ each. Then, for some ...
1 vote
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### The Hamiltonian of a system under only the effect of an electric field

I have a maybe silly doubt: in quantum mechanics, we have the Hamiltonian as kinetic energy + potential energy. Now kinetic energy is obtained from the integral of force and displacement. Potential ...
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### Hamiltonian is conserved, but is not the total mechanical energy

I wondering about the interpretation for the energy difference between the Hamiltonian and the total mechanical energy for systems where the Hamiltonian is conserved, but it is not equal to the total ...
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### Calculation and interpretation of creation/annihilation with basis vector

The two site Fermion Hubbard toy model has the following equation: \begin{equation} {H}^2_F=-t({c}^{\dagger}_{1\uparrow}{c}_{2\uparrow}) \end{equation} Using the basis vector for one electron, \begin{...
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### Hamiltonian symmetry Lie algebra

What is the connection between complete set of commuting observables and generators of the Lie group? I have a Hamiltonian written down in second quantized formalism and I also checked that it ...
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### Criterion for stationary density matrix

A density matrix $\rho$ is time independent iff it commutes with the Hamiltonian $H$. I am wondering if there is a criterion to test whether $[\rho, H] =0$ using some trace condition. Specifically, I ...
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### Why are Eigenvectors of a 1D quantum ising hamiltonian real

I was modelling the 1D transverse quantum Ising model and made a Kronecker product loop to find the Hamiltonian of the system, for a given magnetic field configuration. Now, my question is that when I ...
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