Questions tagged [hamiltonian]
The central term in the hamiltonian formalism. Can be interpreted as an energy input, or "true" energy.
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Second quantization of hamiltonian of the Klein-Gordon field [closed]
Good day everyone. When I try to do a second quantization on the hamiltonian, I end up with the following equation,
$$ H = \int \frac{d^3p}{(2\pi)^3} \omega_{\vec{p}} {a_{\vec{p}}}^{\dagger} {a_{\vec{...
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Why does $e^{-H}\partial_j e^{H} = \partial_j + \partial_jH$?
I apologize if this is a dumb question but I have really thought about this a while and I can’t understand it. I have tried to prove this using the power series of the exponential function but I did ...
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How are propagators for splitting methods applied to time-dependent Hamiltonians derived?
Splitting methods are defined to approximate the solution of the differential equation
$$
y'(t) = (X+Y)y(t), \ \ \ \ \ \ \ t \in (t_0,T) \tag{1}\label{eq:1}
$$
where $X$ and $Y$ are non-commuting ...
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Connection of a concrete Hamiltonian to the generator of time-translations
In a Quantum-mechanics lecture I am hearing we defined the Hamiltonian of a quantum system (a system with an observer) as the generator of the time translation-operation of the system under ...
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How come time does not commute with $i\hbar\dfrac{\partial}{\partial t}$ but it does so with $H$? [duplicate]
Are they not supposed to be the same operator according to Schrödinger equation?
$$
i\hbar\dfrac{\partial}{\partial t}\psi = H\left(\vec{r},-i\hbar\nabla,t\right)\psi
$$
Apparently $[t,i\hbar\dfrac{\...
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How to tell whether Hamiltonian has rotational invariance? Conservation of angular momentum?
If a system contains isotropic exchange interaction and uniaxial anisotropy in the $z$-direction,
does this Hamiltonian satisfy rotational invariance of the $z$-direction so that the spin angular ...
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Uniquness of the vacuum in a theory with/without mass gap
Context
I read the note Light Cone Quantization and Perturbationwritten by Guillance Beuf. He gives a argument in section 3.3.2, p17, 2nd paragraph :
In particular, in a theory with a mass gap, ...
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Multi-particle Hamiltonian for the free Klein-Gordon field
The text I am reading (Peskin and Schroeder) gives the Hamiltonian for the free Klein-Gordon field as:
$$H=\int {d^3 p\over (2\pi)^3}\; E_p\; a^{\dagger}_{\vec p}a_{\vec p}$$
This does not seem to be ...
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Is the Hamiltonian for the transverse field Ising model Hermitian?
I'm watching these lectures in Condensed Matter Physics. At Lec. 13, the lecturer introduces the transverse field Ising model with the Hamiltonian
$$H = - J \sum_i \sigma_i^x \sigma_{i+1}^x - h \sum_i ...
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Sign of momentum doesn't affect Bogoliubov coefficients in Bogoliubov transformation for BEC
I'm running into some issues with the deriving Bogoliubov transformation. Specifically, in order to diagonalize the Hamiltonian
$$\begin{align}H = \sum_p \frac{p^2}{2m} \hat a^\dagger_p \hat a_p + \...
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Complex potential in quantum mechanics
I'm reading Quantum Mechanics by Griffiths. In the solution to one of the problems in this book they claimed that if the time-independent wavefunction $\psi$ solves $-\frac{\hbar}{2m}\frac{\partial^2\...
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Noise in quantum computing
Consider a quantum computer, and one specific qubit $q$ in it. With the computer, we perform a series of operations which manipulate the qubits including $q$. I am interested in the time interval ...
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$\mathbf k\cdot\mathbf p$ Hamiltonian
I am looking into the $k\cdot p$ Hamiltonian approach to describe a semiconductor system. The simplest system appears to be the 2x2 system which can be visualised as: \begin{pmatrix}
\epsilon(k) &&...
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Determining a gapped Hamiltonian from correlation function [closed]
Consider a spin Hamiltonian. I am interested in understanding how the spin-spin correlation function $C(r_{ij}) = \langle \boldsymbol{S}_i \cdot \boldsymbol{S}_j \rangle - \langle \boldsymbol{S}_i \...
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Renormalization of two-sublattice tight-binding Hamiltonian
I have a generic tight-binding Hamiltonian of the form
$$H=\sum_n A c_n^\dagger d_n+Bd_n^\dagger c_n +C c_{n+1}^\dagger d_n + D d_n^\dagger c_{n+1}$$
where $A,B,C,D$ are parameters (hopping amplitudes)...
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