# Questions tagged [hamiltonian]

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

813 questions
Filter by
Sorted by
Tagged with
1answer
50 views

1answer
69 views

### Why does the wave function of a non relativistic particle flatten out over time?

The Hamiltonian I used is the classical one with no potential energy: H=p^2/2m $$i \hbar \frac{\partial \psi}{\partial t} = -\frac{\hbar^2}{2m} \frac{\partial^2 \psi}{\partial x^2}$$ I want to gain ...
1answer
84 views

### Is Hamiltonian a scalar or tensor in Quantum Mechanics?

According to Wikipeida, a scalar operator is invariant under rotations, and the Hamiltonian satisfies this definition. But at the same time, a Hamiltonian can be written as a matrix, which means it is ...
0answers
46 views

### Why is the generalized momentum replaced by the momentum operator but not the ordinary momentum?

I was trying to understand the derivation of the Hamiltonian for a charged particle in an electromagnetic field. https://en.wikipedia.org/wiki/Hamiltonian_mechanics#...
0answers
45 views

### Direct Derivation of Kraus Operator from Interaction Hamiltonian

For the dynamics of open quantum systems, the Kraus operators $K_\kappa$ can be derived from the unitary orbit $U(t)\rho U(t)^\dagger$ for $\rho=\rho_S\otimes\rho_E$ of the composite system given by ...
1answer
77 views

### Significance of energy in a time dependent quantum box

The Hamiltonian for a particle in a finite box is $$H = \frac{p^2}{2m} + V(x)$$ which will give time evolution as $$i\hbar d/dt|{\psi(t)}\rangle = H|{\psi(t)}\rangle \, .$$ However, if I do a ...
0answers
20 views

### (Altland-Simon) Deriving ferromagnetic interaction term from interacting tight-binding Hamiltonian

Below is a part of the book "Condensed Matter Field Theory" by Altland and Simon. My question is about deriving the equation with red arrow. This is outlined in the exercise in the figure, but I don'...
2answers
80 views

### Completeness condition involving continuum states

Consider a potential $V(x)$ in 1d. Suppose that $V(|x| > a )= 0$ for some positive $a$. We then know that the hamiltonian $H = - \frac{\partial^2}{\partial x^2 } + V(x)$ has non-normalizable or ...
0answers
20 views

1answer
48 views

### Calculating exact energy levels of perturbed Hamiltonian

I wish to find the exact energy levels of the following perturbed hamiltonian. $$\hat{H}=\frac{p^2}{2m}+\frac{m\omega^2}{2}x^2+\alpha x+\beta p^2.$$ I believe that it can be solved by using the ...
0answers
40 views

### Expection values of the hamiltonian of Klein-Gordon field

The hamiltonian of the quantized Klein-Gordon field $\phi(\textbf{x},t)$ can be writting using the creation and annihilation operators: \hat{H} = \frac{1}{2} \int d^{3}\textbf{p} \ \omega_{p} (\hat{...
4answers
108 views

### Simultaneous eigenstates of Hamiltonian and momentum operator

Given the potential barrier, \begin{align} V(x, y) = \left\{ \begin{array}{cc} V_{0} & \hspace{5mm} \text{if $0 \leq x \leq D$} \\ 0 & \hspace{5mm} \text{...
1answer
93 views