# Questions tagged [hamiltonian]

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

958 questions
Filter by
Sorted by
Tagged with
46 views

### Conditions of separation of variable of wave function

In quantum mechanics as far as I know when the hamiltonian operator can be written as $$H = H_1 + H_2$$ then the wave function can be written as $$\psi_1 \cdot \psi_2$$ but as we get further in ...
59 views

### Calculation of effective Hamiltonian

I'm stuck with calculating the effective Hamiltonian of a model system. The energy-dependence of the effective Hamiltonian is confusing me a lot. My question is how to treat this dependence ...
26 views

### Can energy eigenstates be in a superposition of quantum numbers?

I know that given say 4 quantum numbers $J^2$, $J_z$, $J_1^2$, $J_2^2$ (e.g. for the Hamiltonian $H=\lambda J_{1}.J{_2}$), the state |$J$,$J_z$,$J_1^2$,$J_2^2$>=|2,2,1,1> will be an energy eigenstate (...
46 views

### Energy degeneracy given a rigid-rotor Hamiltonian

I'm trying to work out the degeneracy of some energy levels in a Hamiltonian given by $H = \frac{1}{2a} (L_x^2 + L_y^2) + \frac{1}{2b} L_z^2$. Looking for a common base of eigenstates $Y_l^m$ ...
124 views

### Numerical calculation of a quantum field's observables

Okay so QFT is definitely beautiful and elegant theory, its mathematics is rich and ingenious, but there is so much one can do with symbolic manipulations of mathematical objects only, how can I ...
59 views

49 views

131 views

### How come the eigenvalues of the Hamiltonian represent energy levels when the Hamilton doesn't represent the energy of the system?

Like in the Hamiltonian for a particle in an electromagnetic field. This is not a conservative field so the Hamiltonian doesn't represent the energy of the system. And yet the time independent ...
45 views

### Effective hamiltonian method for the quantum Ising model

I am reading Subir Sachdevs book on quantum phase transitions (second edition). In chapter 5 (page 58) he defines a hamiltonian $H=H_0+H_1$ where the eigenstates of $H_0$ are known and the influence ...
68 views

73 views

### Derive hamiltonian from equations of motion

Is there a method for deriving the hamiltonian given that you know the equations of motion? For example given the equation (equation 5 in paper linked) they simply the derive the Hamiltonian in ...
66 views

### Spectrum of Dirac Hamiltonian

The Dirac Hamiltonian is given by, \begin{aligned} H &=\sum_s\int \frac{d^{3} p}{(2 \pi)^{3}} E_{\vec{p}}\left[b_{\vec{p}}^{s \dagger} b_{\vec{p}}^{s}+c_{\vec{p}}^{s \dagger} c_{\vec{p}}^{s}\right]...
38 views

26 views

### Balance the units of the following hamiltonian

The following image is taken from an article and shows the hamiltonian of a spin chain model. I knew that the dimensional units in an equation must balance. To ensure this, the author took a procedure ...
77 views

### What happens to the configuration manifold when one quantizes the Hamiltonian?

A system in classical mechanics can be described by a configuration manifold $Q$ and a Lagrangian \begin{equation} L:TQ\rightarrow \mathbb{R} \end{equation} where $TQ$ is the tangent bundle or a ...
When constructing the Lagrangian for a two-component left-handed Weyl field $\psi$, in e.g. Srednicki, one rejects the choice of $\partial^\mu \psi \partial_\mu \psi+\partial^\mu \psi^\dagger \... 0answers 44 views ### “Unnatural” Hamiltonian systems from a statistician's perspective I would like to learn more about "unnatural" Hamiltonian systems, that is, systems whose energies cannot be written as $$H(p,q) = K(q) + U(p).$$ I have seen the term "natural" applied to systems ... 2answers 164 views ### Are the classical hamiltonian and quantum hamiltonian different types of objects? Context: I'm not a physicist. I've come across the Hamiltonian in classical physics and in quantum physics, and I can't recognise why they have the same name. They seem very different. So I probably ... 1answer 116 views ### A non-Hermitian system whose “Hamiltonian” is the annihilation operator Consider a notional quantum system whose "Hamiltonian" is the annihilation operator, $$H=a .$$ Its initial state$|ψ(0)\rangle$is $$|\psi(0)\rangle=\sum_{n=0}^{\infty} c_{n}| n\... 2answers 102 views ### Why is the Hamiltonian of a photon = 0? I'm studying the motion of light near Schwarzschild black holes, and I was wondering why the Hamiltonian of the Schwarzschild metric$$H = - \left( 1-\frac{2M}{r} \right)^{-1} \frac{p_{t}^2}{2}+\left(... 2answers 154 views ### Can any sum of infinitesimal canonical transforms on phase space be obtained from evolution under a static Hamiltonian? Suppose I have a canonical transformation on phase space, which is obtained by evolving a classical Hamiltonian system from time$t=0$to$t=T$, with some arbitrary time-dependent Hamiltonian$H(t)\$. ...
I'm trying to determine the energetic levels of a system with Hamiltonian $$H=-\frac{h^2}{2m}\frac{\partial^2}{\partial \phi^2}$$ And the border condition $$\psi(0)=\psi(2\pi)$$ The eigenvalues ...