Questions tagged [quantum-mechanics]
Numerical methods and problems involving the solution of the Schrodinger equation and related subatomic models.
1
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1answer
131 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
60 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
72 views
Calculate partial trace of an outer product in Python?
I have a python implementation of calculating the partial trace over select dimensions.
...
1
vote
0answers
55 views
Split step Fourier method to solve Schrödinger equation for moving potential
I'm trying to use the excellent Schrodinger Python class by Jake VanderPlas (https://jakevdp.github.io/blog/2012/09/05/quantum-python/) to simulate a wave packet within a moving Gaussian potential. I ...
-2
votes
1answer
149 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
$$v(x) = - \...
2
votes
1answer
54 views
Magnetization Vector from XY Model for an AntiFerromagnetic System
I am working on an XY model and I'm trying to calculate the magnetization and direction for an anti-ferromagnetic (AF) system. So I have a collection of spins in the $XY$ plane represented as vectors ...
3
votes
0answers
84 views
Avoiding divergent solutions with `odeint`? shooting method
I am trying to solve an equation in Python. Basically what I want to do is to solve the equation:
$$
\frac{1}{x^2}\frac{d}{dx}\left(Gam \frac{dL}{dx}\right)+L\left(\frac{a^2x^2}{Gam}-m^2\right)=0
$$
...
4
votes
1answer
78 views
Matrix exponential of hermitian matrix with eigenvectors from generalized eigenvalue problem
I want to calculate the following expression
$$
\exp(-i\Delta t\mathbf{H})
$$
where $\mathbf{H}\in\mathbb{C}^{n\times n}$ is a hermitian matrix. Since I have a highly optimized eigensolver in the code ...
2
votes
1answer
37 views
Two variables integration matlab
I'm trying to solve physical problem in quantum mechanics of helium atoms, the solution require numerical integration over 2 variables. However when i'm trying to run the next code
...
7
votes
1answer
142 views
Non-hermitian discretizations in quantum mechanics
Consider the Schroedinger equation
$$\left(-\frac12\frac{\partial^2}{\partial x^2} + V(x) \right) \psi(x) = E \psi(x)$$
The usual way to solve it is to introduce a discretization of $\psi(x)$. This ...
2
votes
0answers
114 views
Numerical solution to Time-dependent Schrodinger equation with time dependent hamiltonian
Currently I am facing the problem to solve numerically the following equation for a double well harmonic potential:
$iℏ\frac{\partial}{\partial t}ψ(x,t)=−\frac{ℏ}{2m}\frac{\partial ^2}{∂x^2}ψ(x,t)+V(...
2
votes
1answer
66 views
Jump-Diffusion process: practical solver beyond Euler method?
A jump-diffusion process is a stochastic process where both continuous noise (in my case complex Wiener noise $dZ,dZ^*$ such that $dZ^2=dZ^{*2}=0,|dZ|^2=dt$) and discrete Jumps (in my case Poissonian $...
3
votes
1answer
95 views
Normalizing a density matrix at each iteration
I need to numerically evolve a density matrix using this formula(Actually I have more terms but right nows I am starting with this and facing problems):
$$\dot\rho(t) = -i[H(t), \rho(t)]$$
$H(t)$ is ...
1
vote
0answers
51 views
Is there a software package for Quantum Monte Carlo estimation of the exchange correlation functional?
Quantum Monte Carlo (QMC) calculations historically have been used to parameterise the exchange-correlation functionals for Density Functional Theory (DFT). For example, this article explains a way to ...
1
vote
2answers
852 views
Solving the 1D Particle-in-a-Box using C++
I've just finished learning the physics behind the problem and would like to write a program in C++ than can solve the problem. I'm actually stuck at the start. I've quite a bit of research, the ...
3
votes
1answer
337 views
Numerical propagation of a density matrix using Liouville von Neumann equation
I want to look at time evolution of the density matrices of some, very simple, spin systems, but I am having trouble with my approach.
I want to use a simple for-...
1
vote
1answer
107 views
Matrix exponential by eigenvectors - implementation issues
I posted a similar question yesterday but I deleted it since I think that I had to reformulate it after some insights.
I want to calculate
$$
\exp(-i\Delta t\,\mathcal{H}) = V\,\mathrm{diag}(\{\exp(-...
2
votes
2answers
1k 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
101 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
490 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
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0answers
71 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
44 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 ...
2
votes
1answer
1k 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
91 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
57 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
492 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
259 views
Numerical solution of Dirac equation (eigenvalue problem)
Suppose we have equation of the form:
$$H \Psi = E \Psi $$
where $H$ is Dirac Hamiltonian (also my question can be answered by people who are not familiar with Dirac Hamiltonian but familiar with ...
0
votes
1answer
141 views
How to compute matrix representation of $\hat{y}\frac{\partial}{\partial x}$?
I have a 2-dimensional system which I would like to solve numerically (I'm using finite difference method right now), and its an eigenvalue problem. I have a term that looks like $H\psi(x,y) = [-\frac{...
1
vote
0answers
79 views
How to get the eigenvalues of Hamiltonian in an over complete basis
Let $|\psi_i\rangle$, $i=1...N+m$, be a set of overcomplete basis vector in a $N$-dim Hilbert space. The following are known: (Einstein's summation convention assumed)
$$\hat{H}|\psi_i\rangle=H_{ji}|\...
6
votes
2answers
539 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/...
3
votes
2answers
467 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
981 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
98 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
102 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
1k 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 $\phi_m(x)$:
$$
\psi(x,t)=\sum_m \phi_m(x)e^{-iE_mt/\hbar}
$$
...
2
votes
1answer
275 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 ...
-1
votes
1answer
494 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 :
...
1
vote
1answer
1k 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 ...
3
votes
0answers
312 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 ...
7
votes
1answer
176 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 ...
6
votes
1answer
1k views
Computational methods for finding the energy eigenvalues of the time-independent Schrodinger equation with arbitrary potential
I have seen in some papers that the energy levels in some arbitrary potential are specified. How can one find the energy levels in such arbitrary potentials. For example, $V(x)=\sin^2(x/2)$ with $x\in[...
1
vote
2answers
692 views
Parallelization of element-wise matrix multiplication
I use Armadillo as an interface to OpenBLAS. In my current program, I have a loop, in which I do multiplications of the form
...
2
votes
0answers
165 views
Modeling simple laser induced population transfer via adiabatic passage in python
I'm trying to model adiabatic passage between two levels in a three-level atom interacting with two laser fields using Scipy and Numpy..
I'm not sure if my model is wrong due to my incorrectly ...
1
vote
2answers
540 views
Python, numpy and complex functions (PDE's)
Update 4
I have almost given up on getting this right. This is the solution to the time-independent Schrodinger's equation, so the analytical solution is:
$\psi(x,t) = \psi(x,0)e^{\frac{-iE t}{\hbar}}...
1
vote
2answers
493 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 ...
4
votes
3answers
331 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 ...
1
vote
0answers
69 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)] $ ...
1
vote
1answer
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?
$$\sum_{n=2}^{\infty}\frac1{n(n^2-1)} \sum_{k=1}^\infty \frac{(k-1/n)^{2n-2}}{(k+1/n)^{2n+2}}$$
...
3
votes
2answers
112 views
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 ...
5
votes
2answers
249 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 ...
