Questions tagged [quantum-mechanics]
Numerical methods and problems involving the solution of the Schrodinger equation and related subatomic models.
97
questions
2
votes
1answer
105 views
A problem with Poisson equation
I'm computing the Hartree potentials of atoms by solving the Poisson equation and I use hydrogen atom as a test case. The Poisson equation for hydrogen atom in atomic units is given by
$$\nabla^2 V_H =...
0
votes
1answer
59 views
Why is Time evolving block decimation so efficient?
I have a short question about Time evolving block decimation (TEBD). During a lecture I was told that this method is very efficient in evolving 1D quantum spin systems with only nearest neighbor ...
0
votes
1answer
33 views
Integrating Matrix Elements TypeError: f() takes 1 positional argument but 3 were given
I'm working on a linear variational problem for a general PIB and I keep encountering the same problem, and I know its a rather simple solution. Any suggestions?
...
1
vote
1answer
140 views
How can I evaluate more accurate energy eigenvalues from Schrodinger equation using shooting method?
I am trying to use the "shooting method" for solving Schrodinger's equation for a reasonably arbitrary potential in 1D. But the eigenvalues so evaluated in the case of potentials that do not have hard ...
-1
votes
2answers
73 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
96 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
90 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
124 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)$$
My issue is that I don't have the physical background to understand ...
4
votes
1answer
132 views
Recommendation for a fixed-step ODE solver?
My problem involves the solution of a second-order ODE with a fixed-step (input and output). Specifically, this ODE is the radial part of Dirac and Schrödinger equation for a spherical symmetric ...
2
votes
0answers
68 views
Numerical integration of SDE: choice of $dt$ and algorithm
I am working on the following Stochastic Differential Equation (SDE) in the Quantum Mechanics context:
$$dX_{t} = a X_{t} dt + b X_{t} dW$$
where $X_{t}$ is my stochastic varible, $dt$ is my ...
2
votes
1answer
142 views
Numerical solution to the Landau-Zener problem
I tried to use a midpoint method and numerically solve the Schrödinger equation for the original Landau-Zener (LZ) problem: a $2\times 2$ Hamiltonian
$$\left(\begin{array}{c} \alpha t\\ \delta \end{...
2
votes
1answer
157 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
407 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
95 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
116 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
50 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
237 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
256 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
37 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
2k 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
92 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
322 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
394 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
120 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 ...
5
votes
0answers
265 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
177 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
111 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
224 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
386 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
117 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
112 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
57 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
710 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
133 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
$$
\exp(-i\Delta t\,\mathcal{H}) = V\,\mathrm{diag}(\{\exp(-...
5
votes
3answers
4k views
Calculating partial trace of array in NumPy
A simulation I'm doing requires me to calculate the partial trace of a large density matrix. I am trying to calculate it using tools from numpy, but my code seems to be having some problems. For ...
1
vote
0answers
176 views
Second Quantization in Matlab
This question may be more suited for physics.stackexchange, but I saw this post was recommended for StackOverflow or Computational Science, so I'm asking my question here.
I am trying to write a ...
2
votes
2answers
674 views
Schrödinger equation with time dependent Hamiltonian
I need to solve the Schrödinger equation with a time dependent Hamiltonian
$$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
147 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
54 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
99 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
687 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
343 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
157 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
108 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)
$$\hat{H}|\psi_i\rangle=H_{ji}|\...
6
votes
2answers
1k views
Numerical Solution to Schrödinger Equation--Multiple Wells
I am trying to solve for the allowed wavefunctions and energies for a 1D quartic potential well.
To do this I am using the patching method (https://engineering.dartmouth.edu/microeng/otherweb/...
2
votes
2answers
688 views
Zero Eigenvalues in Lanczos Algorithm
I need to find the smallest few eigenvalues of a Hamiltonian (exact diagonalization) I use Python, and SciPy's built-in sparse eigenvalue solver. I notice, however, that for my small system (only a ...
0
votes
1answer
2k views
Solving Time dependent Schrodinger equation using MATLAB ode45 [closed]
The Schrodinger equation for time-dependent Hamiltonian is
$$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 ...
