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About

This library is a reproduction of a project I did as a student of computational chemistry. In essence, the project's goal was to find an answer to

How long does it take for an electron to cross a molecular bridge?

Students of Quantum Mechanics will soon realize that this is question it not even really a valid one. In the realm of QM, there is no such thing as a particle being at "location A". Rather, a particle will have some probability distribution of existing at any location, which is only verifiable upon measurement. When drafting the manuscript for this work, my advisor and myself had considerable difficulty in simply describing the problem in language that wasn't flat-out wrong.

In retrospect, this application is really solving the hitting time of a time-heterogenous markov chain, wherein the transition matrix is the probability that a discretized chunk of probability density is the "object" that is hopping between spatial regions.

This codebase is not the same code that was used in the manuscript, but rather a reimagining that I've done several years later, after much more experience in software development. I did this to see how different the code looks like after some (5 years) of experience in creating software, with 2 of those being professionally.

Working the field of Machine Learning has really opened my eyes to the power of well engineered libraries in the pursuit of science. The deep learning library keras in particular is a triumph of API design greatly accelerating the progress of research in the field.

The problems faced in machine learning and those faced in computational physics and chemistry have an extremely large degree of overlap. While generating this library I've tried to create something that would be intuitive for a domain expert to use.

    from quantized.utils import Parabola
    from quantized.basis import harmonic_basis_from_parabola, HarmonicOscillator, EigenBasis
    from quantized import potentials
    from quantized.time_evolution import TimeEvolvingState
    from quantized.operators import Hamiltonian, Overlap, Kinetic


    parabola = Parabola(a=1.0, b=1.0, c=1.0)
    basis = harmonic_basis_from_parabola(parabola, cutoff_energy=4.0)
    v = potentials.Harmonic(center=0.0, mass=1.0, omega=1.0)
    H = Hamiltonian(v).matrix(basis)
    S = Overlap().matrix(basis)
    eig_basis = EigenBasis.from_basis(basis, H, S)
    initial_state = HarmonicOscillator(n=0, center=parabola.vertex)
    time_evolving = TimeEvolvingState(eig_basis, initial_state)
    kinetic_over_time = time_evolving.observable(Kinetic(), hermitian=True)
    print(kinetic_over_time(t=0))
    print(kinetic_over_time(t=10))

The above is valid, executable code. If I've done my job correctly, this code snippet will be easy for domain experts to understand.