One-dimensional system

We consider a one-dimensional model where the confining potential is parametrized/obtained from finite element calculations. The bare Coulomb interaction is divergent in 1D (REF) and it is customary to use a smoothed Coulomb interaction given by

$$\begin{align} u(x_1, x_2) = \frac{\alpha}{\sqrt{(x_1 - x_2)^2 + a^2}}, \tag{6} \end{align}$$

where $\alpha$ adjusts the strength of the interaction and $a$ removes the singularity at $x_1 = x_2$.

The single-particle functions are chosen as the eigenfunctions of the single-particle Hamiltonian

$$\begin{equation} \left( -\frac{d^2}{dx^2}+v(x) \right) \psi_p(x) = \epsilon_p \psi_p(x). \tag{7} \end{equation}$$

• «
• 1
• ...
• 13
• 14
• 15
• 16
• 17
• 18
• 19
• 20
• 21
• 22
• 23
• 24
• 25
• 26
• 27
• 28
• 29
• 30
• ...
• 43
• »