Numerical integrator

Calculate integral with Newton-Coates/Monte Carlo methods.

Introduction

Codes are written and tested under Python 3.7.1 64-bit with conda environment. Key topic on numerical integration of a 1D quantum-mechanical system. However, you can rewrite main.py to evaluate your own integral.

The wave-function

The 1D QM wave-function is described as

Observable is the probability density of this wave-function, written as:

The probability of observing this wave-function in a specific region [a,b] can be written as:

Dependents

numba package is essential to run the project. It is a package which speeds up the calculation of numpy operations and multithreading loops. This code has a lot of repeated loops and calculations, so numba could translate it into machine code and even parallel computing them. Please use pip install numba or conda install numba, depends on your environment, to install it. numba version 0.41.0 used.

In the case you do not want to use numba, you need to remove codes from numba import jit,njit,prange, @jit(nopython=True) and @njit(parallel=True) in file main.py and monte_carlo.py. Also, replace prange() with range() since automatic parallelization is used to speed up the loop.

Other essential packages:

• numpy: basic mathematical package
• matplotlib: for diagrams
• random: random number generator for Monte Carlo process

How to use

python main.py and you will see instructions on your terminal.

File structure

• The main.py contains the wavefunction and entry of arguments of integrator.
• newton_coates.py and monte_carlo.py contains codes relating numerical integration methods used. No need to run them since they are imported in the main.py.