Schrödinger API - RESTful web service for solving multidimensional time-independent Schrödinger equation using Hermite DVR approach

Developers: Bojana Koteska

Project Supervisors: Anastas Mishev

Scientific Advisors: Ljupco Pejov

Contributors: Thanks to Vojdan Kjorverziroski for his help in deploying the code.

Overview

This RESTful web service (SchrodingerAPI) provides a method for solution of one-dimensional, two-dimensional and three-dimensional time-independent Schrödinger equation based on the the Gauss-Hermite Discrete Variable Representation (DVR) approach.

The solution of one-dimensional (1D) Schrödinger equation is illustrated in the case of following model potentials:

• Morse potential;
• Simple Harmonic Oscillator (SHO) potential;
• Sombrero potential (Mexican hat);
• Woods-Saxon potential.

Solutions of two-dimensional (2D) and three-dimensional (3D) Schrödinger equations are illustrated for the following two model potentials: multidimensional Morse potential and multidimensional SHO potential.

Software metadata

Domain

Computational Physics

Funder

European Commission under the Horizon 2020 - NI4OS-Europe, grant agreement no. 857645

Progamming languages

Python 3, Java

Date created

2024-05-22

Keywords

REST API, RESTful web service, Schrödinger equation

Service description

All service methods are GET methods and they can be tested by entering the parameters directly on the SchrodingerAPI home page (supported by Swagger) at https://schrodinger.chem-api.finki.ukim.mk/. Other possibilites to test the service methods include using browser URL bar, consuming the service methods in your source code or by using specific API testing tools such as Postman.

For example, if user wants to test the 1dHermiteSho method directly at https://schrodinger.chem-api.finki.ukim.mk/, the first step is to click the 1dHermiteSho method from the list :

Then, user should click the button Try it out:

Next, user should enter the parameters (or use the default ones) and click the Execute button. The parameters for each method are presented in the next section.

The results will be shown in the Response Body form below. User can download or copy them.

Other way to use these REST API methods is to access it directly from the browser address bar.

If no parameters are provided, the default parameter values will be taken into consideration. For example, for the 1dHermiteSho method the link should be:

https://schrodinger.chem-api.finki.ukim.mk/1dHermiteSho

If user wants to change only the default parameters npts and k and to provide his/hers, the URL should look like this:

https://schrodinger.chem-api.finki.ukim.mk/1dHermiteSho?npts=10&k=1

If user preffers to change other paramerets, they can be added with the &PARAMETER=VALUE

One of the options is also to consume the method in the user program source code. Examples in Python are provided in the section below.

Build, Installation, and Execution Instructions

Prerequisites

• Ensure you have Java Development Kit (JDK) 8 or later installed. You can download it from here.
• Ensure you have Apache Maven installed. You can download it from here.
• Ensure you have Python 3 installed. You can download it from here.

Supported Environments

This project is compatible with Windows, macOS, and Linux distributions. Ensure that you have Python and Java installed and configured properly on your system.

Build Instructions

To build this project, ensure you have Maven installed on your system. Clone the Repository, Navigate to the Project Directory, and Build the Project with Maven:**

bash git clone https://github.com/bojanakoteska/SchrodingerAPI.git && cd SchrodingerAPI && mvn clean package

Installation Instructions

Once the build is successful, you can run the JAR file in the target directory:

bash java -jar SchrodingerAPI.jar

This command will start the application locally, and you can access it at http://localhost:8080.

Execution Instructions

To interact with the Schrödinger API locally, make sure you have the requests library installed. You can install it using pip:

python pip install requests You can also use the requirements.txt file and run the command:

python pip install -r requirements.txt

Here's an example using Python to make a GET request to "http://localhost:8080/2dHermiteSho":

```python

import requests

Define the URL endpoint

url = "http://localhost:8080/2dHermiteSho"

Make a GET request to the endpoint

response = requests.get(url)

Check if the request was successful (status code 200)

if response.statuscode == 200: # Print the response content print(response.content.decode('utf-8')) else: print("Error:", response.statuscode)

``` To interact with the API online, check the examples in the next subsections.

Examples of the DVR method for solution of one-dimensional (1D) Schrödinger equation

1D Morse potential

Returns a one-dimensional Morse potential V(x):

$V(x)=D \cdot {1-exp[-a\cdot(x-x_0)]}^2-D$

Parameters:

• npts - number of points (default value 10)
• D - dissociation depth(default value 3.0)
• a - inverse "width" of the potential (default value 0.5)
• x0 - equilibrium bond distance (default value 0.0)
• prec - precision (default value 6)

Example with default parameters:

python import requests response = requests.get('https://schrodinger.chem-api.finki.ukim.mk/1dHermiteMorse') if response.status_code == 200: print(response.content.decode('utf-8')) else: print("None")

Example with parameters (npts=10, D=3.0, a=0.5, x0=0.0, prec=6):

python import requests response = requests.get('https://schrodinger.chem-api.finki.ukim.mk/1dHermiteMorse?npts=20&D=0.176&a=1.02&x0=1.4&prec=32') if response.status_code == 200: print(response.content.decode('utf-8')) else: print("None")

1D SHO potential

Returns a one-dimensional harmonic oscillator potential V(x) with wavenumber k:

$V(x)=\frac{1}{2} k\cdot (x-x_0)^2$

Parameters:

• npts - number of points (default value 5)
• k - wavenumber of the SHO potential (default value 1.0)
• x0 - displacement from origin (default value 0.0)
• prec - precision (default value 8)

Example with default parameters:

python import requests response = requests.get('https://schrodinger.chem-api.finki.ukim.mk/1dHermiteSho') if response.status_code == 200: print(response.content.decode('utf-8')) else: print("None")

Example with parameters (npts=10, k=1.0, x0=0.0, prec=19):

python import requests response = requests.get('https://schrodinger.chem-api.finki.ukim.mk/1dHermiteSho?npts=20&k=1.0&x0=0.0&prec=19') if response.status_code == 200: print(response.content.decode('utf-8')) else: print("None")

1D Sombrero potential

Returns a one-dimensional version of the sombrero potential and requires a < 0 and b > 0

$V(x)=a\cdot x^2+b\cdot x^4$

Parameters:

• npts - number of points (default value 5)
• a - coefficient of the x^2 term (default value -5)
• b - coefficient of the x^4 term (default value 1.0)
• prec - precision (default value 8)

Example with default parameters:

python import requests response = requests.get('https://schrodinger.chem-api.finki.ukim.mk/1dHermiteSombrero') if response.status_code == 200: print(response.content.decode('utf-8')) else: print("None")

Example with parameters (npts=10, a=-5.0, b=1.0, prec=3):

python import requests response = requests.get('https://schrodinger.chem-api.finki.ukim.mk/1dHermiteSombrero?npts=10&a=-5.0&b=1.0&prec=3') if response.status_code == 200: print(response.content.decode('utf-8')) else: print("None")

1D Woods-Saxon potential

Returns a Woods-Saxon potential

$V(r)=-\frac{V0}{{1+exp[\frac{(r-R)}{z}]}} ;R=r0 \cdot A^{1/3}$

Parameters:

• npts - number of points (default value 5)
• V0 - potential depth (default value 50.0)
• z - surface thickness (default value 0.5)
• r0 - rms nuclear radius (default value 1.2)
• A - mass number (default value 16)
• prec - precision (default value 8)

Example with default parameters:

python import requests response = requests.get('https://schrodinger.chem-api.finki.ukim.mk/1dHermiteWoodSax') if response.status_code == 200: print(response.content.decode('utf-8')) else: print("None")

Example with parameters (npts=10, V0=50.0, z=0.5, r0=1.2, A=16, prec=4):

python import requests response = requests.get('https://schrodinger.chem-api.finki.ukim.mk/1dHermiteWoodSax?npts=10&V0=50.0&z=0.5&r0=1.2&A=16&prec=4') if response.status_code == 200: print(response.content.decode('utf-8')) else: print("None")

Examples of the DVR method for solution of two-dimensional (2D) Schrödinger equation

2D Morse potential

Returns a two-dimensional Morse potential V(x,y):

$V(x,y)=D1\cdot {1-exp[-a1\cdot(x-x0)]}^2-D1+D2\cdot{1-exp[-a2\cdot(y-y0 )]}^2-D2$

Parameters:

• npts - number of points (default value 5)
• D1 - dissociation depth for x(default value 3.0)
• a1 - inverse "width" of the potential for x(default value 0.5)
• x0 - equilibrium bond distance for x (default value 0.0)
• D2 - dissociation depth for y(default value 3.0)
• a2 - inverse "width" of the potential for y(default value 0.5)
• y0 - equilibrium bond distance for y (default value 0.0)
• prec - precision (default value 6)

Example with default parameters:

python import requests response = requests.get('https://schrodinger.chem-api.finki.ukim.mk/2dHermiteMorse') if response.status_code == 200: print(response.content.decode('utf-8')) else: print("None")

Example with parameters (npts=10, D1=3.0, a1=0.5, D2=3.0, a2=0.5, x0=0, y0=0, prec=100):

python import requests response = requests.get('https://schrodinger.chem-api.finki.ukim.mk/2dHermiteMorse?npts=10&D1=3.0&a1=0.5&D2=3&a2=0.5&x0=0.0&y0=0.0&prec=100') if response.status_code == 200: print(response.content.decode('utf-8')) else: print("None")

2D SHO potential

Returns a two-dimensional harmonic oscillator potential V(x, y) with wavenumber k.

$V(x,y)=\frac{1}{2} k\cdot[(x-x0)^2+(y-y0)^2]$

Parameters:

• npts - number of points (default value 5)
• k - wavenumber of the SHO potential (default value 1.0)
• x0 - x displacement from origin (default value 0.0)
• y0 - y displacement from origin (default value 0.0)
• prec - precision (default value 8)

Example with default parameters:

python import requests response = requests.get('https://schrodinger.chem-api.finki.ukim.mk/2dHermiteSho') if response.status_code == 200: print(response.content.decode('utf-8')) else: print("None")

Example with parameters (npts=5, k=1.0, x0=0.0, y0=0, prec=20):

python import requests response = requests.get('https://schrodinger.chem-api.finki.ukim.mk/2dHermiteSho?npts=10&k=1.0&x0=0.0&y0=0.0&prec=20') if response.status_code == 200: print(response.content.decode('utf-8')) else: print("None")

Examples of the DVR method for solution of three-dimensional (3D) Schrödinger equation

3D Morse potential

Returns a three-dimensional Morse potential V(x,y,z):

$V(x,y,z)=D1\cdot {1-exp[-a1\cdot(x-x0)]}^2-D1+D2\cdot{1-exp[-a2\cdot(y-y0)]}^2-D2+D3\cdot{1-exp[-a3\cdot(z-z0)]}^2-D_3$

Parameters:

• npts - number of points (default value 5)
• D1 - dissociation depth for x(default value 3.0)
• a1 - inverse "width" of the potential for x(default value 0.5)
• x0 - equilibrium bond distance for x (default value 0.0)
• D2 - dissociation depth for y(default value 3.0)
• a2 - inverse "width" of the potential for y(default value 0.5)
• y0 - equilibrium bond distance for y (default value 0.0)
• D3 - dissociation depth for z(default value 3.0)
• a3 - inverse "width" of the potential for z(default value 0.5)
• z0 - equilibrium bond distance for z (default value 0.0)
• prec - precision (default value 6)

Example with default parameters:

python import requests response = requests.get('https://schrodinger.chem-api.finki.ukim.mk/3dHermiteMorse') if response.status_code == 200: print(response.content.decode('utf-8')) else: print("None")

Example with parameters (npts=10, D1=3.0, a1=0.5, D2=3.0, a2=0.5, D3=3.0, a3=0.5, x0=0, y0=0, prec=10):

python import requests response = requests.get('https://schrodinger.chem-api.finki.ukim.mk/3dHermiteMorse?npts=10&D1=3.0&a1=0.5&D2=3&a2=0.5&D3=3.0&a3=0.5&x0=0.0&y0=0.0&z0=0&prec=10') if response.status_code == 200: print(response.content.decode('utf-8')) else: print("None")

3D SHO potential

Returns a three-dimensional harmonic oscillator potential V(x, y, z) with wavenumber k.

$V(x,y,z)=\frac{1}{2} k\cdot[(x-x0)^2+(y-y0)^2+(z-z_0)^2]$

Parameters:

• npts - number of points (default value 5)
• k - wavenumber of the SHO potential (default value 1.0)
• x0 - x displacement from origin (default value 0.0)
• y0 - y displacement from origin (default value 0.0)
• z0 - z displacement from origin (default value 0.0)
• prec - precision (default value 8)

Example with default parameters:

python import requests response = requests.get('https://schrodinger.chem-api.finki.ukim.mk/3dHermiteSho') if response.status_code == 200: print(response.content.decode('utf-8')) else: print("None")

Example with parameters (npts=10, k=1.0, x0=0.0, y0=0, z0=0, prec=15):

python import requests response = requests.get('https://schrodinger.chem-api.finki.ukim.mk/3dHermiteSho?npts=10&k=1.0&x0=0.0&y0=0.0&z0=0.0&prec=15') if response.status_code == 200: print(response.content.decode('utf-8')) else: print("None")

License

This project is licensed under the MIT License; for more details, see the LICENSE file.