Branches

fockflow: the frozen Fock Flow version, see CanWeFlowStateByState.md for more instruction.

singleflow: the oringinal style flow, environment ready for production.

1D Quantum

Originated from July, 2024, served as a internship object.

Problem

Try to solve a one-dimensional quantum mechanic problem with Hamiltonian

$$ \hat H = -\frac{1}{2} \nabla^2 + \hat V $$

with the following potential

$$ V(x) = 3x^4 + \frac{1}{2} x^3 - 3x^2 $$

Some hints on units:

The ground state wavefunction and ground state energy is our target.

• Left:
  • Born-Oppenheimer: the potential plotted with x as x axis.
  • Exact solution: the exact ground state energy.
• Right:
  • The probability density (square of wavefunction) w.r.t. x.

Implementation

Finite Differential

See ./FiniteDifferential/FD_1DSchordinger.py

Using finite differential method to directly constructing Hamiltonian and Exact Diagonalizing it.

Get the ground state wavefunction and ground state energy.

Then compare it with the reference above.

NOTE: Please try to rewrite the numpy code using jax!

VMC (Flow)

See VMC/main.py

A good VMC reference: reference/ML_for_Materials_Hard_and_Soft_ML_for_Ab_initio_Electronic_Structure_Tutorial_(Solution).ipynb

Which is cloned from this repo.

Try to use VMC with a Gaussian-based-normalizing-flowed wavefunction ansatz, calculate the variational ground state.

Bonus: calculating the excited states.