Tagged Questions

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

131 views

Zero Eigenvalues in Lanczos Algorithm

I need to find the smallest few eigenvalues of a Hamiltonian (exact diagonalization) I use Python, and SciPy's built-in sparse eigenvalue solver. I notice, however, that for my small system (only a ...
27 views

I want to solve an equation of the form $$\left[\frac{d^2}{d r^2} + \frac{1}{r}\frac{d}{d r}\right]\psi = 0$$ where $\psi$ is a wave function using finite difference method. The equation is more ...
75 views

Solving Time dependent Schrodinger equation using MATLAB ode45 [on hold]

The Schrodinger equation for time-dependent Hamiltonian is $$i\hbar\frac{d}{dt}\psi(t) = H(t)\psi(t) \, .$$ I try to implement solve the Schrodinger equation for time-dependent Hamiltonian in ODE ...
46 views

Solving Schrodinger's Equation Numerically in a Bunimovich Stadium

I need to solve, as mentioned, Schrodinger's equation in a Bunimovich stadium-shaped infinite potential well with Dirichlet BC Numerically (this isn't possible analytically). In order to do so, I need ...
9 views

Starting structure for stacking interaction energy calculation

I have a crystal structure (single crystal, pyranone carboxamide derivative) that shows $\pi$-$\pi$ stacking, and I want to do theoretical calculations. I am using Dispersion-correcting potentials (...
43 views

Quantum Chemical Calculations is there a book for which method to use with what problem?

Does anyone know of a book that will outline which quantum chemical methods are appropriate for what problems? I am trying to make informed choices before I start using computational resources. It is ...
180 views

imaginary time propagation to find ground state wavefunction

I understand the basic idea of imaginary time propagation method: The wavefunction $\psi(x,t)$ as a superposition of energy eigenstates $\phi_m(x)$: $$\psi(x,t)=\sum_m \phi_m(x)e^{-iE_mt/\hbar}$$ ...
87 views

ground state from the Schroedinger equation with a central potential what happens to the origin

I have code that attempts to implement a solution to the Schrödinger equation where there is a central potential (more or less im thinking of hydrogen), in 1-D using the numerov method to construct ...
39 views

Gaussian and external basis set. How to write the input correctly [closed]

I have to use the LANL2DZpd basis set. It can be obtained from EMSL Basis Set Exchange. But trying to calculate simple Me2Se molecule : ...
296 views

Transfer Matrix Method in a rectangular potential well

I am trying to follow an algorithm that is described in Elementary Quantum Mechanics in 1D. I want to compute eigen-energies and functions in bound states in the basic case in rectangular potential ...
193 views

C60 orbital calculation

I am currently trying to reproduce the results published by Hands et al.1 using MATLAB. They calculated the bases of the C60 wave functions of HOMO, LUMO and LUMO+1. I did the following: I ...
112 views

Forcing an ODE solver to preserve the norm

I have an ODE of the form $$\frac{dy}{dt} = -i H y \enspace .$$ where $y$ is a complex vector and $H$ is a time dependent Hermitian matrix. The norm of the solution $y(t)$ at any point in time ...
195 views

251 views

Integrating radial Schrodinger equation with Lennard-Jones potential using Runge-Kutta with adaptive step size ends up with a step-size of zero

I'm currently taking a course in computational physics. I'm new to computational physics and programming in general. I'm using numerical recipes to try and integrate the radial Schrodinger equation ...
262 views

Propagating Schrodinger equation

My task is to simulate quantum evolution. To do that I need to perform this operation $$w = e^{-itH}v$$ where $H$ is a sparse matrix and $v$ is the initial column vector. I am wondering if there is ...
55 views

Solving condensate density problem in MATLAB

I want to solve for $n_{0}$ for a fixed value of $n$, lets say $n=1$ $$n= n_{0}+ \dfrac{1}{2}\int_{-1/2}^{1/2}dq\left(\dfrac{e_{q}+Un_{0}}{\hbar\omega}-1\right)$$ where $e_{q}=2[1-cos(2\pi q)]$ ...
59 views

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? $$\sum_{n=2}^{\infty}\frac1{n(n^2-1)} \sum_{k=1}^\infty \frac{(k-1/n)^{2n-2}}{(k+1/n)^{2n+2}}$$ ...
72 views

Solve numerically inwards and outwards the radial equation?

We have the Schrodinger eqn $$(−\Delta+V(r))R(r)=E R(r)$$ 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 ...
125 views

Transparent boundary conditions for finite element simulation of TDSE

I have implemented a version of Visscher's method for numerically solving the TDSE (A fast explicit algorithm for the time-dependent Schrödinger equation) (also described in Are there simple ways to ...
43 views

Modifying finite difference solution to Schrodinger eqn to account for fermion/boson effects

I have been playing with an implementation of Visscher's explicit method for solving the time dependent Schrodinger equation (Are there simple ways to numerically solve the time-dependent Schö...
64 views

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 $N$ ...
87 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 ...
252 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 ...
897 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 ...
126 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 ...
1k 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: ...
211 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 ...
1k 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 ...
1k 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. ...
244 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 ...
397 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 ...
345 views

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 ...
985 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 ...
258 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 ...
236 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 ...
183 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 ...
2k 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 ...
100 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 method,...
365 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:  ...
632 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 ...
117 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 ...
92 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 ...
360 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 ...
139 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 ...
515 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 ...