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:
Use the following command lines to install:
git clone https://github.com/tttianhao/Schrodinger.git
cd schrodinger
python setup.py install
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
- Revise the Hamiltonian
- Handle unevenly distributed position Inputs