1
vote
1answer
44 views

Calculate Euler equations of fluid dynamics without division?

I'm working on the calculation of the Euler equations with the finite volume method. Unfortunately I'm not allowed to do a division. So I'm wondering if there's a form which does not need a division. ...
4
votes
1answer
136 views

Numerical analytic continuation for Green's function

Recently, I happened to hear about the possibility of doing analytic continuation numerically. That sounds attractive for the ubiquitous $\mathrm{i}\omega_n\rightarrow\omega+\mathrm{i}0^+$ procedure, ...
4
votes
1answer
66 views

Discretizing the Wave Equation in polar coordinates

I want to discretize the wave equation $$\frac{1}{c^2}\frac{\partial^2\psi\left(\vec{r},t\right)}{\partial t^2}=\triangle\psi\left(\vec{r},t\right)$$ in polar coordinates. I find the following ...
7
votes
1answer
186 views

Numerical schemes, time integration algorithms and energy conservation

What does it mean when someone says a numerical scheme or a time integration algorithm is "energy conserving". How can a numerical scheme "gain" or "lose" or "conserve" energy apart from the numerical ...
0
votes
0answers
62 views

numerical diagonalisation comparison of complex Hermition matrix and real matrix

we are doing K space calculation(transnational invariant basis) of Hamiltonian, and trying to compare with exact method for same nos of sites and particles, we are getting big difference in ground ...
2
votes
2answers
202 views

numerical formulation of Dirac equation plus electromagnetic field

I have the following equations describing the electron field in a (classic) electromagnetic field: $$ c\left(\alpha _i\right.{\cdot (P - q(A + A_b) + \beta mc) \psi = E \psi } $$ where $A_b$ is ...
3
votes
3answers
316 views

Can a wavefunction be solved to any arbitrary precision, given enough computer time?

I learned that the wavefunction for the hydrogen atom can be solved analytically (we did the derivation in class), but that for more complicated atoms it is "impossible" to solve and that only ...
5
votes
0answers
496 views

Interpretation of Stiffness Matrix and Mass Matrix in Finite Element Method

I would like to have a general interpretation of the coefficients of the stiffness matrix that appears in FEM. For instance if we are solving a linear elasticity problem and we modelize the relation ...
0
votes
1answer
517 views

Calculating Kramers-Kronig using Mathematica

First of all, I know there is a Mathematica group in beta, but I don't think the problem of the following is directly a Mathematica issue. I am trying to calculate the change of the refractive index ...
1
vote
1answer
239 views

Numerical algorithms to generate a random wavefunction from a thermal ensemble

I am seeking an algorithm to generate a random wavefunction = $\sum {c_i |\varphi _i\rangle }$ from a thermal ensemble, whose density matrix $\rho \sim e^{-\beta H}$, without the need to diagonalize ...
4
votes
1answer
336 views

Numeric method to calculate the charge distribution on a conducting surface?

If I have an arbitrary (closed?) conducting surface and a nearby charge density, is there a simple numeric way of computing the induced charge distribution on the surface?
12
votes
1answer
2k views

Solving Schrödinger's equation with Crank-Nicolson method

I am trying to numerically solve Schrödinger's equation with Cayley's expansion ($\hbar=1$) $$\psi(x,t+\Delta t)=e^{-i H\Delta t}\psi(x,t)\approx\frac{1-\frac{1}{2}i H\Delta t}{1+\frac{1}{2}i H\Delta ...