# Questions tagged [hamiltonian]

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

1,568 questions
Filter by
Sorted by
Tagged with
1 vote
24 views

### Quasi-periodic motion of $N$-particle systems [closed]

My question is about the time evolution of multi-particle systems in QFT. There are such systems evolving a-periodically. I struggle with the treatment of them, always obtaining periodic or quasi-...
56 views

### Do different Hamiltonians result in different ground states?

I'm learning density functional theory. In the proof of Hohenberg–Kohn theorem I, we assume that different Hamiltonians result in different ground states. Is it true? In general, for example, we can ...
1 vote
49 views

• 63
171 views

• 129
37 views

### Derivative term in chain of LC coupled oscillators Hamiltonian

I am taking quantum superconducting circuits course and I cannot recover a formula provided by the lecturer. I want to calculate the Hamiltonian of the following distributed element model of coplanar ...
• 848
85 views

### How to derive the formal solution of Heisenberg's equation? [closed]

In the book Introductory to Quantum Optics https://ostad.hormozgan.ac.ir/ostad/UploadedFiles/386042/386042-1758823246346514.pdf, we have that for an arbitrary operator $\hat{O}$ having no explicit ...
100 views

60 views

### On time-evolution of a quantum state

Suppose I have a quantum system governed by a time-independent Hamiltonian $H$. Its eigenvectors $\{|\varphi_n\rangle\}_{n\in\mathbb{N}}$ form a complete orthonormal set (or basis) for the Hilbert ...
• 1,374
56 views

• 121
66 views

### Condition for stationary density matrix

I have a question about section 5 in 'Statistical mechanics' (Pathria). According this book, the density matrix (operator) should satisfy the following identity, which describes the time evolution of ...
• 33
47 views

• 1,346
62 views

### Factorization of 1d Ising model partition function

If I'm studying a 1-dimensional Ising model such that $\mathcal H = \sum_k J_k\sigma_k\sigma_{k+1}$, where $$J_k=\begin{cases}J&k \in2\mathbb N\\2J&k\in2\mathbb N+1 \end{cases}$$ can I ...
• 137
35 views

### Propagator for radial force field?

The propagator $K(x,y;t)$ is well known for the (1D) harmonic oscillator: $$H = -\frac{\hbar^2}{2m}\frac{\partial^2}{\partial x^2} + \frac{m}{2}\omega^2 x^2$$ is there a simple closed form solution ...
• 6,510
1 vote
47 views

### Hamiltonian and Thermal Energy

I was reviewing my lessons when I read this definition on Thermal Energy: The sum of potential energy and kinetic energy is equal to Thermal Energy But isn't this the same as the Hamiltonian? So, ...
• 157
### How does $[H,H] = 0$ imply $dH/dt = 0$?
I have a conceptual question about how $[H,H] = 0$ implies $dH/dt = 0$. Does this relation work for both time-dependent and -independent Hamiltonians, or a general observable $H$?
Working on some QM and we realised we don't understand the simple equation is for the wavefunction. $H \psi(x) = E \psi(x)$ We know $H$ is the hamiltonian, the sum of the kinetic and potential ...