Numerical methods and problems involving the solution of the Schrodinger equation and related subatomic models.
Numerical methods and problems involving the solution of the Schrodinger equation.
Questions tagged [quantum-mechanics]
128 questions
13
votes
1 answer
Numerical Methods for the Schrodinger Equation
We are comparing the performance of various numerical methods that can be used to solve the Schrodinger's Equation for the Hydrogen Atom interacting with a strong laser pulse (too strong to use perturbation methods). When using discretization…
Amanda Crawford
- 131
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7
votes
2 answers
How to numerically solve a laser driving semi-classical two-level system using Floquet formalism?
Consider the semi-classical laser driving two-level atom, where the laser is treated classically and the atom is treated quantum mechanically. The effect of laser on the atom is a dipole…
xslittlegrass
- 345
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3
votes
0 answers
Hamiltonian Matrix Size in Schrodinger Equation
I'm attempting to solve the particle-in-a-box problem using Scipy (with the help of http://www.physics.buffalo.edu/phy410-505/2011/topic4/app2/index.html). At first, I used a 16x16 matrix to model the Hamiltonian, like the link, and my results…
Shivam Sarodia
- 131
- 2
3
votes
1 answer
Numerical solution to the Landau-Zener problem
I tried to use a midpoint method and numerically solve the Schrödinger equation for the original Landau-Zener (LZ) problem: a $2\times 2$ Hamiltonian
$$\left(\begin{array}{c} \alpha t\\ \delta \end{array}\begin{array}{c} \delta \\-\alpha t …
Yuval Tamir
- 31
- 1
3
votes
2 answers
Solve numerically inwards and outwards the radial equation?
We have the Schrodinger eqn
\begin{equation}(−\Delta+V(r))R(r)=E R(r)\end{equation}
where we can take $V(r)=-k/r$ for the beginning and we impose on the reduced radial function $u(r)=r R(r)$ the boundary conditions $u(0)=u(\infty)=0$.
The problem is…
wondering
- 141
- 6
2
votes
1 answer
Split operator FFT quantum dynamics for a harmonic oscillator
I would like to do a numerical quantum dynamics of a displaced gaussian in harmonic oscillator using split-operator method (see bottom of these notes by Hal Evans for the algorithm).
I have a problem with the step (3). I'm not sure how to represent…
kirill_igum
- 71
- 5
2
votes
1 answer
Numerov method for Schrodinger equation
While learning about numerical methods for solving the Schrödinger equation I came across Numerov's method.
I want to get the solution for the harmonic oscillator by alreading giving the eigenvalues. The algorithm requires that I know two initial…
ben tenyson
- 21
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2
votes
1 answer
Monte Carlo normalization of a wave function
I would like to normalize a quantum mechanical multi-particle wave function numerically, and since the result is a multidimensional integral I thought Monte Carlo methods might be appropriate. So, I'm looking for $\mathcal{N}$…
jorgen
- 123
- 4
1
vote
2 answers
Computing eigen-decomposition of several matrices in parallel in C++
I am writing a program in C++ in which I am trying to reduce the run-time by computing eigen-decomposition of several matrices in parallel. This might be a programming question but since many Physics people might use it, I am asking the question…
cleanplay
- 121
- 2
1
vote
1 answer
Is it possible to eliminate the inner sum to evaluate numerically?
Any hints on how to simplify the following double sum to be able to find the sum at least numerically?
$$\sum_{n=2}^{\infty}\frac1{n(n^2-1)} \sum_{k=1}^\infty \frac{(k-1/n)^{2n-2}}{(k+1/n)^{2n+2}}$$
Series comes from quantum mechanics (2nd order…
wondering
- 141
- 6
0
votes
1 answer
How to get a Wannier function of tight-binding model numerically (i.e. Python)
I have a question on construction of a Wannier function for tight-binding model. Let's say we consider the tight-binding model of 1D chain with two atoms( site A and B in a unit cell). In k-space we can write the single-particle Hamiltonian in…
Ricky Pang
- 101