# Questions tagged [hamiltonian]

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

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### Correspondence between quantum operators and classical formulas

Background From what knowledge of quantum mechanics I have so far, it is a postulate that Hermitian operators corresponding to a certain observable act on a quantum state $\psi$ to produce a new ...
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### Connection between Hamiltonian and density matrix

I found this equation in my notes from a seminar on BCS theory $$H_{m,n} = \frac{dE}{d\rho_{n,m}}$$ where $H_{m,n}$ are elements of the Hamiltonian in matrix representation, $\rho_{n,m}$ are ...
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### Hamiltonian of charged particle in an EM field and magnetic field does no work on charged particles

I am trying to understand a part of I.E.P.'s answer here. I.E.P. states that one can see from the following Hamiltonian, $$H = \frac{1}{2m}|{\bf p}+q{\bf A}|^2 +q \phi \tag{8.35}$$ that the magnetic ...
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### How is Hamilton's first equation useful in solving mechanics problems? [duplicate]

Here is the first Hamilton equation: $\frac{\partial H}{\partial {p}_q} = \dot{q}$ Let's use it. Imagine a ball rolling down a frictionless hill (ignore the friction vector in the image). As time goes ...
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### Hamiltonian of a particle in magnetic field squared

I'm trying to follow Tong lectures about Gauge Theories, but I think I'm doing some really stupid mistake. At one point he takes the Hamiltonian for a spin $1/2$ particle in a potential as the usual \...
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### Transverse field Ising in 2 dimensional lattice - kronecker product

Assume we have a transverse field Ising chain (1D): $\hat H =-J\sum_{i=1}^{N}\sigma^z_i\sigma^z_{i+1}-h\sum_{i=1}^{N}\sigma^x_i$, where $\sigma^{\alpha}_i$ are the local spin operators at site i ...
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### Decoupling theory by diagonalising the Hamiltonian

I have a Hamiltonian of the form $H = 2k(\alpha \alpha^* -\beta \beta^*) -2\lambda (\alpha\beta^* + \beta \alpha^* )$ and I'd like to decouple the $\alpha$'s and $\beta$'s if possible. I know I need ...
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### Deriving the Hamiltonian of the Klein-Gordon field in terms of ladder operators (Peskin and Schroeder 2.31)

In Peskin and Schroeder's QFT book they give \begin{align*} H &= \int d^3x\int \frac{d^3p d^3 p'}{(2\pi)^6}e^{i(\mathbf{p+p'})\cdot \bf x}\left\{-\frac{\sqrt{\omega_{\bf p}\omega_{\bf p'}}}{4} (a_{...
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### The “basic hamiltonian” of topological systems

I am currently studying topological insulators and repeatedly found the claim (e.g. here), that the "basic hamiltonian" of a topological system in $d$ spatial dimensions can be written using ...
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### Canonical ensemble: Why do I lose dependency on the number of particles N here?

I have a problem understanding the solution of an exercise that deals with a gas in the framework of the canonical ensemble. Because I'm not a native english speaker some sentences might sound a bit ...