Questions tagged [quantum-mechanics]
Numerical methods and problems involving the solution of the Schrodinger equation and related subatomic models.
94
questions
-1
votes
2answers
45 views
2d Schrodinger Equation via matrix diagonalization in C
I am trying to solve the time-independent Schrodinger equation in two dimensions via discrete matrix diagonalization. I want the energy eigenvalues and the corresponding eigenfunctions for a given ...
-1
votes
1answer
85 views
If not MATLAB, what software/programming language should I use to simulate/animate wave functions in various potentials + more? (example given)
I want to integrate programming into my learning in math and science in a very specific way. I want to create visualizations and simulations of concepts I am learning. When I learn a numerical method ...
1
vote
1answer
76 views
Operator splitting to solve time dependent Schrödinger equation
I encountered the split operator method to solve the time dependent Schrödinger equation during a lecture. I understand the method on a theoretical basis (I think at least), but I'm struggling to ...
3
votes
1answer
89 views
Numerical solution of zero-potential time-dependent Schrödinger equation in 1D
I want to solve numerically the one-dimensional time-dependent Schrödinger equation $$i \psi_t(x,t)=-\frac{\hbar}{2m} \psi''(x,t)$$
My issue is that I don't have the physical background to understand ...
4
votes
1answer
111 views
Recommendation for a fixed-step ODE solver?
My problem involves the solution of a second-order ODE with a fixed-step (input and output). Specifically, this ODE is the radial part of Dirac and Schrödinger equation for a spherical symmetric ...
2
votes
0answers
60 views
Numerical integration of SDE: choice of $dt$ and algorithm
I am working on the following Stochastic Differential Equation (SDE) in the Quantum Mechanics context:
$$dX_{t} = a X_{t} dt + b X_{t} dW$$
where $X_{t}$ is my stochastic varible, $dt$ is my ...
1
vote
1answer
103 views
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
$$\left(\begin{array}{c} \alpha t\\ \delta \end{...
0
votes
1answer
109 views
Numerov method for Schrodinger equation
While learning about numerical methods for solving the Schrödinger equation I came across Numerov's method.
I want to get the solution for the harmonic oscillator by alreading giving the eigenvalues. ...
1
vote
1answer
231 views
What will be the impact of quantum computing on existing numerical techniques (e.g. CFD)?
Quantum computing seems to be a very active and promising development area in computer science. However, I am curious as to what impact (if any) quantum computing will have on existing classical ...
0
votes
1answer
63 views
How to do Weierstrass-transform in MATLAB?
I have a diagonalization problem. I have the eigenstates correctly, and I want to do a Gaussian-smearing (Weierstrass-transform) on them. So I have the wave functions ($\Psi$), and the continuous ...
0
votes
0answers
41 views
Boundary conditions for solving the time-independent SE for the hydrogen atom
I am trying to solve the schrodinger equation for the hydrogen atom numerically, using finite elements, with matlab's solvepdeeig(). I have a hard time getting the solution to be right, and it seems ...
0
votes
0answers
86 views
Finding second excited state of Schrödinger equation with secant Runge Kutta method
In our assignment, we are required to find the energies of the ground state and the first two excited states of the Schrödinger equation in a harmonic potential:
$$V = \frac{50 x^2}{(10^{-11})^2}\, .$...
1
vote
0answers
37 views
How to numerically calculate the transition dipole integral in periodic systems?
Now I have wave functions $\psi_a$ and $\psi_b$ of two states in Gaussian CUBE format. I'd like to evaluate the transition dipole moment integral $\pmb\mu$ between these two states. As my simulation ...
3
votes
1answer
226 views
MATLAB: Faber approximation of the matrix exponential to solve Liouville-von-Neumann equation
EDIT: I moved the full code to my github page so the post can be read more easily.
I am writing a script to take the Faber approximation approach outlined in Hassan Fahs paper (free access)
and apply ...
2
votes
1answer
176 views
Incorporating a potential barrier in a wave-packet simulation (Fourier Transform method)
I'm trying to simulate the scattering of a wave-packet at a potential barrier in Python. I'm using a Fourier Transform method (not sure if its the same as the Split-Step method), where I apply Fourier ...
1
vote
0answers
33 views
Hydrogen-like wavefunction as starting guess for atomic solver?
I've been looking into radial solvers for quantum wave equations (Schroedinger and Dirac). In both cases, the suggestion seems to be to go with the "shooting method", with integration schemes of ...
1
vote
1answer
1k views
Double potential well with Python
I'm trying to understand the Schrödinger equation and solving it a bit better, and I'm running into some doubts while coding, even though I am adapting the code to this situation. Also I tried asking ...
2
votes
1answer
86 views
Discrepancies between numerical and analytical solution for particle in a finite potential well?
Analytical
Inside the box, the wavefunction is:
\begin{equation}
\frac{\hbar^2}{2m} \frac{d^2 \psi(x)}{dx^2} = E \psi(x) \iff
\frac{d^2 \psi(x)}{dx^2} = k^2 \psi(x)
\end{equation}
where $k = \...
1
vote
1answer
235 views
Calculate partial trace of an outer product in Python?
I have a python implementation of calculating the partial trace over select dimensions.
...
-2
votes
1answer
264 views
Solving Schrodinger equation numerically
Here is the Schrodinger equation that is to be solved:
A 1D hard wall potential in $[0, 1]$. The potential within the potential well is given by a linear combination of Gaussian dips
$$v(x) = - \...
2
votes
1answer
111 views
Magnetization Vector from XY Model for an AntiFerromagnetic System
I am working on an XY model and I'm trying to calculate the magnetization and direction for an anti-ferromagnetic (AF) system. So I have a collection of spins in the $XY$ plane represented as vectors ...
3
votes
0answers
225 views
Avoiding divergent solutions with `odeint`? shooting method
I am trying to solve an equation in Python. Basically what I want to do is to solve the equation:
$$
\frac{1}{x^2}\frac{d}{dx}\left(Gam \frac{dL}{dx}\right)+L\left(\frac{a^2x^2}{Gam}-m^2\right)=0
$$
...
4
votes
1answer
118 views
Matrix exponential of hermitian matrix with eigenvectors from generalized eigenvalue problem
I want to calculate the following expression
$$
\exp(-i\Delta t\mathbf{H})
$$
where $\mathbf{H}\in\mathbb{C}^{n\times n}$ is a hermitian matrix. Since I have a highly optimized eigensolver in the code ...
2
votes
1answer
92 views
Two variables integration matlab
I'm trying to solve physical problem in quantum mechanics of helium atoms, the solution require numerical integration over 2 variables. However when i'm trying to run the next code
...
7
votes
1answer
207 views
Non-hermitian discretizations in quantum mechanics
Consider the Schroedinger equation
$$\left(-\frac12\frac{\partial^2}{\partial x^2} + V(x) \right) \psi(x) = E \psi(x)$$
The usual way to solve it is to introduce a discretization of $\psi(x)$. This ...
2
votes
0answers
269 views
Numerical solution to Time-dependent Schrodinger equation with time dependent hamiltonian
Currently I am facing the problem to solve numerically the following equation for a double well harmonic potential:
$iℏ\frac{\partial}{\partial t}ψ(x,t)=−\frac{ℏ}{2m}\frac{\partial ^2}{∂x^2}ψ(x,t)+V(...
2
votes
1answer
93 views
Jump-Diffusion process: practical solver beyond Euler method?
A jump-diffusion process is a stochastic process where both continuous noise (in my case complex Wiener noise $dZ,dZ^*$ such that $dZ^2=dZ^{*2}=0,|dZ|^2=dt$) and discrete Jumps (in my case Poissonian $...
3
votes
1answer
111 views
Normalizing a density matrix at each iteration
I need to numerically evolve a density matrix using this formula(Actually I have more terms but right nows I am starting with this and facing problems):
$$\dot\rho(t) = -i[H(t), \rho(t)]$$
$H(t)$ is ...
1
vote
0answers
53 views
Is there a software package for Quantum Monte Carlo estimation of the exchange correlation functional?
Quantum Monte Carlo (QMC) calculations historically have been used to parameterise the exchange-correlation functionals for Density Functional Theory (DFT). For example, this article explains a way to ...
1
vote
2answers
2k views
Solving the 1D Particle-in-a-Box using C++
I've just finished learning the physics behind the problem and would like to write a program in C++ than can solve the problem. I'm actually stuck at the start. I've quite a bit of research, the ...
3
votes
1answer
637 views
Numerical propagation of a density matrix using Liouville von Neumann equation
I want to look at time evolution of the density matrices of some, very simple, spin systems, but I am having trouble with my approach.
I want to use a simple for-...
1
vote
1answer
121 views
Matrix exponential by eigenvectors - implementation issues
I posted a similar question yesterday but I deleted it since I think that I had to reformulate it after some insights.
I want to calculate
$$
\exp(-i\Delta t\,\mathcal{H}) = V\,\mathrm{diag}(\{\exp(-...
4
votes
2answers
3k views
Calculating partial trace of array in NumPy
A simulation I'm doing requires me to calculate the partial trace of a large density matrix. I am trying to calculate it using tools from numpy, but my code seems to be having some problems. For ...
1
vote
0answers
156 views
Second Quantization in Matlab
This question may be more suited for physics.stackexchange, but I saw this post was recommended for StackOverflow or Computational Science, so I'm asking my question here.
I am trying to write a ...
2
votes
2answers
644 views
Schrödinger equation with time dependent Hamiltonian
I need to solve the Schrödinger equation with a time dependent Hamiltonian
$$i\hbar \frac{\partial}{\partial t} \Psi = \left[-\frac{\hbar^2}{2m}\nabla^2 +\frac{1}{2} k(t)(x^2+y^2) + V(r)\right]\Psi $...
1
vote
0answers
128 views
lightweight implementation of semiempirical quantum chemistry (e.g. MNDO,AM-1,PM3)
I'm searching for semi-empirical quantum chemistry solver which would be easy to integrate into my own software. I found a few implementations which can be in principle used e.g. MOPAC, ORCA, SQM some ...
1
vote
0answers
53 views
Parallelizing molecular simulation with full configuration energy
First, let just me stress that I'm not a an expert in computation chemistry, so now the problem:
We have GCMC molecular simulation, in the Grand Canonical ensemble, using the standard metropolis ...
4
votes
1answer
2k views
Simple open-source Quantum chemistry or DFT code in C/C++
I know lot of density functional packages in fortran, including one which we are developing in our group (Fireball-DFT) but I don't like fortran very much and I would like something which is easier ...
0
votes
1answer
97 views
Stability of dark solitons in a harmonic trap
This question is based upon a research article which I am trying to reproduce. One of the main result of this paper is the condition on transverse confinement of the Bose-Einstein Condensate(BEC) to ...
1
vote
0answers
87 views
constrained quadratic binary problems and quantum adiabatic evolution
I'm going through an article with title "Solving constrained quadratic binary problems via quantum adiabatic evolution" (reference 1). And there are several points confusing me a lot.
This article is ...
0
votes
1answer
648 views
Best books and notes for beginners in the parallel FORTRAN 90 programming
I am a PhD student and my field of study is Quantum Information and Computation in the theoretical aspect. Actually I write the computer codes/program in FORTRAN 90 which are serial codes but now I ...
2
votes
0answers
329 views
Numerical solution of Dirac equation (eigenvalue problem)
Suppose we have equation of the form:
$$H \Psi = E \Psi $$
where $H$ is Dirac Hamiltonian (also my question can be answered by people who are not familiar with Dirac Hamiltonian but familiar with ...
0
votes
1answer
149 views
How to compute matrix representation of $\hat{y}\frac{\partial}{\partial x}$?
I have a 2-dimensional system which I would like to solve numerically (I'm using finite difference method right now), and its an eigenvalue problem. I have a term that looks like $H\psi(x,y) = [-\frac{...
1
vote
0answers
101 views
How to get the eigenvalues of Hamiltonian in an over complete basis
Let $|\psi_i\rangle$, $i=1...N+m$, be a set of overcomplete basis vector in a $N$-dim Hilbert space. The following are known: (Einstein's summation convention assumed)
$$\hat{H}|\psi_i\rangle=H_{ji}|\...
6
votes
2answers
962 views
Numerical Solution to Schrödinger Equation--Multiple Wells
I am trying to solve for the allowed wavefunctions and energies for a 1D quartic potential well.
To do this I am using the patching method (https://engineering.dartmouth.edu/microeng/otherweb/...
2
votes
2answers
620 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 ...
0
votes
1answer
2k views
Solving Time dependent Schrodinger equation using MATLAB ode45 [closed]
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 ...
2
votes
0answers
127 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 ...
0
votes
3answers
121 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 ...
1
vote
1answer
2k 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 $\phi_m(x)$:
$$
\psi(x,t)=\sum_m \phi_m(x)e^{-iE_mt/\hbar}
$$
...
