# Questions tagged [hamiltonian]

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

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### Confusion about why deducing pointer observable from the structure of the Hamiltonians is not practical

I am trying to learn Zurek's theory of decoherence. Right now I am reading Decoherence, einselection and the existential interpretation (the rough guide) which seems like an easier read than his big ...
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### What is the physical meaning of expectation value of the Hamiltonian operator?

I've been studying David Griffiths' Introduction to Quantum Mechanics and int that, it was explained that the expectation value of position $x$ is the average of the positions of $N$ identically ...
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### Hermitian conjugate in Hubbard model hopping term

I'm new to Hubbard model and I have a few questions about it. From the sources I can find on the internet, Fermionic-Hubbard model is often written as (please correct me if I'm wrong!) \begin{align} H ...
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### Hamiltonian for particle moving in a sphere

Context: I know that if we have a particle (say, with unit mass) moving in the plane $\Bbb R^2$ subject to a spherically symmetric potential $V\colon \Bbb R^2 \to \Bbb R$, it will move along the ...
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### Hamiltonian diagonalisation using quantum Fourier transform [closed]

Here is a problem to solve: diagonalize the following hamiltonian using quantum fourier transform. The hamiltonian reads: $$\sum_{i,j=1}^N e^{-\theta_{ij}} c_i^\dagger c_j + h.c.$$ Where $c_j$ are ...
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### Is the Hamiltonian of a relativistic charged particle in an electromagnetic field only an approximation?

Consider a system of two relativistic charged point particles 1 and 2 which interact through their electric and magnetic fields. The equation of motion for the first particle is then given by the ...
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### Time evolution of operators with explicit time dependence in case of time dependent Hamiltonian

In case of a time dependent Hamiltonian of the sort $$H=\frac{p^2}{2m}+\frac{1}{2}m \omega(t) x^2$$ I have solved for the time evolution operator using the Schrodinger equation and got $U(t,0)$. If, I ...
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### How do contact transformations differ from canonical transformations?

From Goldstein, 3rd edition, section 9.6, page 399 after equation 9.101: [...] The motion of a system in a time interval $dt$ can be described by an infinitesimal contact transformation generated ...
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### Time dependent Hamiltonian operator and $SU(1,1)$ generator method

In this screenshot of a paper I am reading, I have the following question: 1.What is a $SU(1,1)$ group and how do we find its generators? 2.From the expression for the Hamiltonian $\hat{H}$, how do ...
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### A fundamental question about Time-dependent Hamiltonians

I have a fundamental question about Quantum Mechanics or even mechanics in general. I am aware that there are stationary solutions and non-stationary solutions. The stationary solutions solve ...
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### What is the unitary matrix that diagonalizes the Hamiltonian?

If $H = H_0 + g H_1$ is our (free + interaction) Hamiltonian, and we assume that we have a basis of states $\{ | i \rangle \}$ under which $H_0$ is diagonal, then we may diagonalize $H$ by some ...
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### State of a system at previous time

If I am given the state of a quantum system at $t=0$ as $| \psi \rangle$ and I know the Hamiltonian $H$ of the system for time $t<0$, how can I write the state of the system at some time $t<0$?
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### Inverse of canonical quantization: Classical kinetic energy corresponding to a Laplacian on a sphere

In canonical quantization, we replace the canonical conjugate of position($x$), $p$ by $-i \hbar\frac{d}{dx}$. In general we replace $\mathbf{p}$ by $-i\hbar \nabla$. My question is, what if I wanted ...
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### Harmonic oscillator in microcanonical ensemble

Consider a hamiltonian of a simple classical pendulum $$H=p^2+\omega q^2.$$ How can quantities such as $\langle p^2 \rangle$ or $\langle q^2\rangle$ can be calculated using the microcanonical ...