Wikimedia Commons

File:Hartree-Products vs Slater-Determinants.png

Original file ‎(735 × 739 pixels, file size: 108 KB, MIME type: image/png)

Captions

Captions

Add a one-line explanation of what this file represents

Summary

edit
Description
English: Four contour plots illustrating the different behaviour of a 1-D Wavefunction of two electrons created from a Hartree-Product and a Slater-Determinant under exchange of the two electrons
Deutsch: Vier Konturplots die den Unterschied im Verhalten einer 1-D-Wellenfunktion für zwei Elektronen illustrieren, die als Hartree-Produkt oder als einer Slater-Determinante angesetzt wurde, wenn die beiden Elektronen vertauscht werden.
Date
Source Own work
Author Lpd-Lbr

Generated with
Python 3.7.1
matplotlib 3.0.2

import numpy as np
from matplotlib import pyplot as plt
import math

def gaussian(x, alpha):
    return math.exp(-alpha*x*x/2)

gridpoints = np.arange(0, 100, 1)
posr1 = 25
alpha1 = 0.01
posr2 = 75
alpha2 = 0.01
gamma = 1
HP1 = [[gaussian(r1 - posr1, alpha1)*gaussian(r2 - posr2, alpha2) for r1 in gridpoints] for r2 in gridpoints]
HP2 = [[gaussian(r2 - posr1, alpha1)*gaussian(r1 - posr2, alpha2) for r1 in gridpoints] for r2 in gridpoints]
SD1 = np.array(HP1) - np.array(HP2)
SD2 = np.array(HP2) - np.array(HP1)

%matplotlib inline

fig, axs = plt.subplots(2, 2, figsize=(12, 12), gridspec_kw = {"wspace": 0.25, "hspace": 0.45})

for column in axs:
    for subplot in column:
        subplot.set_xticks([25,75])
        subplot.set_xticklabels(["Atom 1", "Atom 2"], fontsize = 18)
        subplot.set_yticks([25,75])
        subplot.set_yticklabels(["Atom 1", "Atom 2"], fontsize = 18, rotation = "vertical", verticalalignment = "center")
        subplot.set_xlabel("Position of Electron 1", fontsize = 20)
        subplot.set_ylabel("Position of Electron 2", fontsize = 20)

axs[0,0].contour(gridpoints, gridpoints, HP1)
axs[0,0].set_title("Hartree-Product", fontsize = 24)
axs[1,0].contour(gridpoints, gridpoints, HP2)
axs[1,0].set_title("Exchanged\nHartree-Product", fontsize = 24)
axs[0,1].contour(gridpoints, gridpoints, SD1)
axs[0,1].set_title("Slater-Determinant", fontsize = 24)
axs[1,1].contour(gridpoints, gridpoints, SD2)
axs[1,1].set_title("Exchanged\nSlater-Determinant", fontsize = 24)
plt.show()

Licensing

edit
I, the copyright holder of this work, hereby publish it under the following licenses:
GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.
w:en:Creative Commons
attribution
This file is licensed under the Creative Commons Attribution 3.0 Unported license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
You may select the license of your choice.

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current14:46, 29 October 2019Thumbnail for version as of 14:46, 29 October 2019735 × 739 (108 KB)Lpd-Lbr (talk | contribs){{Information |description ={{en|1=Four contour plots illustrating the different behaviour of a 1-D Wavefunction of two electrons created from a Hartree-Product and a Slater-Determinant under exchange of the two electrons}} {{de|1=Vier Konturplots die den Unterschied im Verhalten einer 1-D-Wellenfunktion für zwei Elektronen illustrieren, die als Hartree-Produkt oder als einer Slater-Determinante angesetzt wurde, wenn die beiden Elektronen vertauscht werden.}} |date =2019-10-29 |sou...

You cannot overwrite this file.

The following page uses this file:

File usage on other wikis

The following other wikis use this file:

Metadata

This file contains additional information such as Exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it. If the file has been modified from its original state, some details such as the timestamp may not fully reflect those of the original file. The timestamp is only as accurate as the clock in the camera, and it may be completely wrong.

Retrieved from "https://commons.wikimedia.org/w/index.php?title=File:Hartree-Products_vs_Slater-Determinants.png&oldid=718941830"