Tagged Questions
2
votes
2answers
132 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
223 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 ...
0
votes
0answers
76 views
Coupled decay behavior? [closed]
I solved the following "coupled" ODE numerically, whit forward Euler scheme:
$$
\frac{\text{d}N_a}{\text{d}t} = -\frac{N_a}{\tau_a}
$$
$$
\frac{\text{d}N_b}{\text{d}t} = ...
4
votes
0answers
346 views
Interpretation of Stiffness Matrix and Mass Matrix in Finite Element Method
I would like to have a general interpretation of the coefficients of the stiffness matrix that appears in FEM. For instance if we are solving a linear elasticity problem and we modelize the relation ...
0
votes
1answer
396 views
Calculating Kramers-Kronig using Mathematica
First of all, I know there is a Mathematica group in beta, but I don't think the problem of the following is directly a Mathematica issue.
I am trying to calculate the change of the refractive index ...
1
vote
1answer
170 views
Numerical algorithms to generate a random wavefunction from a thermal ensemble
I am seeking an algorithm to generate a random wavefunction = $\sum {c_i |\varphi _i\rangle }$ from a thermal ensemble, whose density matrix $\rho \sim e^{-\beta H}$, without the need to diagonalize ...
3
votes
1answer
214 views
Numeric method to calculate the charge distribution on a conducting surface?
If I have an arbitrary (closed?) conducting surface and a nearby charge density, is there a simple numeric way of computing the induced charge distribution on the surface?
8
votes
1answer
2k views
Solving Schrödinger's equation with Crank-Nicolson method
I am trying to numerically solve Schrödinger's equation with Cayley's expansion ($\hbar=1$)
$$\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 ...
