Numerical methods and problems involving the solution of the Schrodinger equation and related subatomic models.

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Extract the correlation matrix from Monte Carlo data

I am writing my undergrad thesis on the harmonic oscillator on a lattice. So far I have implemented the Metropolis Monte Carlo algorithm to generate trajectories $x_j$ for $0 \leq j < N$, where $N$ ...
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0answers
42 views

Recursive code that uses Newton's method to calculate bands of the Kronig Penney model [closed]

Can someone help or give me some input writing a program (matlab) preferable, that will recursively calculate the bands of the Kronig Penney model? Unfortunately, I haven't taken any computer class ...
2
votes
1answer
60 views

Why do QM programs use redundant internal coordinates for geometry optimization?

Brief explanation of QM geometry optimization Quantum mechanics packages are often tasked with optimizing a chemical structure. The problem is essentially this: Given a set of points in 3D space and ...
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4answers
233 views

Are there simple ways to numerically solve the time-dependent Schödinger equation?

I would like to run some simple simulations of scattering of wavepackets off of simple potentials in one dimension. Are there simple ways to numerically solve the one-dimensional TDSE for a single ...
2
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1answer
100 views

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 ...
2
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1answer
224 views

Implementation of the Numerov Method for the 1D square well

I want to solve the Schrodinger via the Numerov Method but I had some troubles. I'm programing in C++, so here is my code: ...
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1answer
108 views

Partial trace algorithm [duplicate]

In general, is there a partial trace algorithm (ideally for systems of any size) that can be coded using basic matrix operations found in software like Mathematica or Maple? All of the methods I'm ...
3
votes
1answer
203 views

Partial trace algorithm (original)

In general, is there a partial trace algorithm (ideally for systems of any size) that can be coded using basic matrix operations found in software like Mathematica or Maple? All of the methods I'm ...
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vote
4answers
351 views

Best PARALLEL numerical solver of first order differential equation

I have a system of 256 differential equations that I want to solve numerically. The system represents the Liouville equation, which is a first order, linear differential equation with complex numbers. ...
3
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1answer
155 views

A programming model for Quantum Mechanics angular momenta in Mathematica

I'm writing prototypes for solving the Liouville Equations with Mathematica and C++. Perhaps the question about this may not be suited for this forum in a strict way, but it suits the people here ...
2
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1answer
188 views

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 ...
9
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2answers
297 views

Confusion about Quantum Monte Carlo

My question is about extracting observables from QMC methods, as described in this reference. I understand the formal derivation of various QMC methods like Path Integral Monte Carlo. However, at the ...
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3answers
330 views

Energy level diagram - software

Which easy-to-handle software would you recommend me for creating energy level diagrams? What do you use and what is your experience? I'm recently working on my bachelor thesis and I would like to add ...
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2answers
210 views

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 ...
2
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2answers
162 views

Nanoseconds vs. picoseconds in numerical quantum problems with Matlab ODEs

Hello there and thanks for taking a look at this problem. This problem is related to my previous question and I will therefore use a similar introduction from, Choice of step size using ODEs in ...
2
votes
1answer
74 views

Time-dependent wavefunction numerical simulator

I want to develop a visual simulation of a propagating 2D wavefunction with an added attractive potential. Basically I have to numerically solve the time-dependent Schrodinger equation (PDE with x,y,t ...
9
votes
3answers
599 views

Choice of step size using ODEs in matlab

Hey there and thanks for giving time to look at my question. This is a updated version of my question which I posted earlier in physics.stackexchange.com I'm currently studying a 2D exciton spinor ...
2
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1answer
72 views

What FCIQMC codes are out there?

Full configuration interaction quantum Monte Carlo seems like it is poised to overtake DFT in some applications pretty soon. I am curious if there is any freely available implementation of the ...
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2answers
197 views

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 coupling: $$ ...
6
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1answer
263 views

Why is it difficult to numerically solve multi-electron time-dependent Schrödinger's equation

It seems that people usually use the Single Active Electron (SAE) approximation to deal with a multi-electron system, transforming the problem into a single electron problem. For example, in ...
2
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1answer
110 views

Trying to generate a wave function basis set

For a little project I'm working on, I am trying to generate a wavefunction basis set I can use in Quantum Monte Carlo (DMC to be specific). Preferably, it would be a linear combination of Slater ...
3
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2answers
78 views

What is the difference in accuracy between fully QM atomic simulations vs QM + classical?

If I want to do a very accurate simulation of a molecular system (e.g. 2 hydrogen atoms), then I'll want to use something like diffusion Monte Carlo to determine the energies of these atoms in ...
3
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0answers
203 views

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 ...
3
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1answer
126 views

What is a good introduction to mixed quantum-classical modelling

Currently, I have some experience with classical molecular dynamics simulations, and I've had undergraduate course in quantum mechanics (the course was "analytical" one, no approaches to computer ...
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1answer
363 views

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 ...
4
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1answer
603 views

How to find Lyapunov exponent for coupled system

Answer gives a software for calculating conditional lyapunov exponent (CLE) for coupled oscillators in chaos synchronization. However, its hard to follow and there is no graphical output of the plot ...
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2answers
101 views

Are there any QM macromolecule simulation methods that can use an electron density map as input?

I am not an xray crystallographer, but from what I've heard there's often a good deal of guess work and intuition involved in the process of fitting a ball-and-stick molecular model to a ...
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7answers
774 views

Where do the laws of quantum mechanics break down in simulations?

As someone who holds a BA in physics I was somewhat scandalized when I began working with molecular simulations. It was a bit of a shock to discover that even the most detailed and computationally ...