tttianhao / Schrodinger

Schrodinger Equation

Overview

This project solves the lowest energy state and its wave function of a particle in a given potential field by Schrodinger Equation using Fourier basis set. The Schrodinger Equation is:

where H is an operator that maps L2 to L2 and the inner product on L2 space is defined as:

the Hamiltonian operator on a given wave function is defined as:

Installation

Use the following command lines to install:

git clone https://github.com/tttianhao/Schrodinger.git

cd schrodinger

python setup.py install

Usage

Inputs:

• --size:

  • Int, The size of the fourier basis set: {1, sin(x), cos(x), sin(2x), cos(2x)...}
  • default is 5

• --c:

  • Float, The constant in the Hamiltonian
  • default is 1

• --file:

  • String, The path and file name of the potential energy
  • optinal argument, default is schrodinger/potential_energy.dat
  • note: please begin the first line of the data file with "#" and the first column being position, second column being potential energy.
  • The position input has to be evenly distributed.

• --domain:

  • String, the domain of position
  • default is the domain of the input position data
  • note: please input the domain in the format of 'a,b' (seperate lower and upper bound by comma)
  • The domain input has to be within the range of position data

TODO

• Revise the Hamiltonian
• Handle unevenly distributed position Inputs