Linked Questions
11 questions linked to/from Complex valued 2+1D PDE Schrödinger equation, numerical method for `NDSolve`?
0
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Time evolution of a wave packet from the time-independent Schroedinger equation [duplicate]
Starting off with the time-independent Schroedinger equation (TISE)
$\quad \quad
-\frac{\hbar^2}{2m} \nabla^2 \psi + V(r, \theta) \psi = E\, \psi,$
I would like to study the time evolution of an ...
80
votes
3
answers
10k
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Numerically solving Helmholtz equation in 2D for arbitrary shapes
I would like to solve the Helmholtz equation with Dirichlet boundary conditions in two dimensions for an arbitrary shape (for a qualitative comparison of the eigenstates to periodic orbits in the ...
- 1,018
22
votes
4
answers
3k
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Only final result from NDSolve
Finally, I started to play with differential equations in Mathematica.
And I have faced the problem, which seems to me so basic that I'm afraid this question is going to be closed soon. However, I'...
- 138k
13
votes
1
answer
4k
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Schrödinger eigenvalue problem in two dimensions (Harmonic Oscillator)
I read here the discussion about how to solve a one-dimensional eigenvalue problem. I am wondering, how can one generalize these methods to two dimensions?
For example, how to solve this equation:
$$...
- 145
11
votes
2
answers
1k
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Wonky Solutions to Schrödinger Equation with Box Barrier
I'm trying to solve the Schrödinger equation using NDSolve in a case where there is a potential box barrier. The initial condition is a cosine wave, and for ...
- 581
17
votes
1
answer
2k
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Frequency domain Maxwell equations with PML boundary conditions
I'm trying to solve a full-vectorial wave equation for an arbitrarily shaped wave guide, by using NDSolve and perfectly matched layer (PML) conditions.
The PML ...
- 1,275
11
votes
1
answer
929
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Modelling the effect of a structure on a "tsunami" (hyperbolic wave equation)
So, the hyperbolic wave equation can be quite easily solved in Mathematica like this:
...
- 5,391
13
votes
1
answer
1k
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Complex valued 2+1D nonlinear PDE using NDSolve
I am trying to follow the main ideas presented in this question, applying it to my own problem, which is a complex, time-dependent, nonlinear PDE:
$$i \frac{\partial \psi}{\partial t} = \left[ -\...
- 901
8
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2
answers
719
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Using NDSolve`StateData without processing it into rule
Problem
I need to solve a differential equation system. Nothing fancy here so far with the issue of too less memory on my machine. The interpolation functions I get from ...
- 842
3
votes
1
answer
256
views
1
vote
0
answers
174
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NDSolve for complex pde
My goal is to use NDSolve to solve the complex pde $F(z,t)$ with complex derivative $\partial_{z}=\frac{1}{2}(\partial_{x}-i \partial_{y}).$ The equation can be ...
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