TimeIndependentSchrodingerEquation

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Julia package repository to resolve Time-Independent Schrödinger equation by (F)init (E)lement (M)ethod. This is an implementation of Gridap package for unidimensional and bidimensional grids.

Project carried out in my PhD studies of Physics at:

• Faculty of Mathematics, Astronomy, Physics and Computation (FaMAF)
• The Enrique Gaviola Institute of Physics (IFEG)

Check here The GitHub Page

Warning!

->> The package is under construction <<-

How we can use TimeIndependentSchrodingerEquation package ?

1. Clone TimeIndependentSchrodingerEquation package

First we need to clone package from GitHub repository as follow

    @prompt$: cd ~/my_directory/
    @my_directory$: git clone https://github.com/mendzmartin/TimeIndependentSchrodingerEquation.jl.git

This will download a folder called TimeIndependentSchrodingerEquation.jl, it is important to keep the .jl extension in the repository name. And, in case we have already cloned the repository, we must update it by running git pull.

2. Build Julia code to use TimeIndependentSchrodingerEquation package

    @prompt$: mkdir ~/my_folder
    @prompt$: cd ~/my_folder
    @my_folder$: julia
               _
   _       _ _(_)_     |  Documentation: https://docs.julialang.org
  (_)     | (_) (_)    |
   _ _   _| |_  __ _   |  Type "?" for help, "]?" for Pkg help.
  | | | | | | |/ _` |  |
  | | |_| | | | (_| |  |  Version 1.9.0 (2023-05-07)
 _/ |\__'_|_|_|\__'_|  |  Official https://julialang.org/ release
|__/                   |

    julia> Ctrl+]
    (@v1.9) pkg>
    (@v1.9) pkg> activate .
    (@my_folder) pkg> instantiate()
    (@my_folder) pkg> dev ~/my_directory/TimeIndependentSchrodingerEquation.jl
    (@my_folder) pkg> add Revise
    julia> exit()

then build Julia code with following structure:

module MyModule

using Pkg
Pkg.activate("./")
Pkg.instantiate()

using TimeIndependentSchrodingerEquation
using Revise

#=
... ...
    code block where we use function
    from TimeIndependentSchrodingerEquation package
... ....
=#

end

Then we save de Julia code below name MyModule.jl. After that, we can run the code doing this

    @my_directory$: julia MyModule.jl

Also, if we have activated multi-thread configuration we can use the next command to activate parallelism:

    @my_directory$: julia -t 4 MyModule.jl

where we have specified 4 threads as parallelization.

Run from Julia REPL

We can also run the package directly from Julia REPL by opening the terminal Ctrl+Alt+T inside the package folder and typing the following commands inside the terminal:

    @prompt$: cd my_directory/TimeIndependentSchrodingerEquation.jl/
    @TimeIndependentSchrodingerEquation.jl$: julia
               _
   _       _ _(_)_     |  Documentation: https://docs.julialang.org
  (_)     | (_) (_)    |
   _ _   _| |_  __ _   |  Type "?" for help, "]?" for Pkg help.
  | | | | | | |/ _` |  |
  | | |_| | | | (_| |  |  Version 1.9.0 (2023-05-07)
 _/ |\__'_|_|_|\__'_|  |  Official https://julialang.org/ release
|__/                   |

    julia> Ctrl+]
    (@v1.9) pkg>
    (@v1.9) pkg> activate .
    (@my_folder) pkg> instantiate()
    (@my_folder) pkg> dev ~/my_directory/TimeIndependentSchrodingerEquation.jl
    (@my_folder) pkg> add Revise
    julia> using TimeIndependentSchrodingerEquation
    julia> using Revise

and then we can, for example, access Julia's help mode to ask for specific package functions such as the following:

    julia> Shift+?
    help?> space_coord
    search: space_coord

    if dimension=="1D" ⇒ dom=(x₁,x₂); Δr=Δx; n=nx
    if dimension=="2d" ⇒ dom=(x₁,x₂,y₁,y₂); Δr=(Δx,Δy); n=(nx,ny)

Examples

See some use examples in test folder where you can find some uses of TimeIndependentSchrodingerEquation package's functions.

Here you can see some plots from Package's simulations eg.:

Unidimensional Symmetric Finit Kronig-Penney

Unidimensional Quantum Harmonic Oscillator	Bidimensional Isotropic Quantum Harmonic Oscillator

Unidimensional Morse Potential: Morse parameter vs Eigen energies	Unidimensional Finit Well Potential: Depth potential vs Eigen energies

Contact

Please, contact the project administrator Méndez Martín for any improve suggestion or questions about package use.