SPS-QM-2D

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Single Particle States - Quantum Mechanics in 2D

SPS-QM-2D 최신버젼 다운로드

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# Single Particle States in 2D

Various simulations of non-relativistic single particle quantum mechanics in bounded 2D potentials.
The eigenstates animation are inspired by the [awesome art](https://www.instagram.com/hudthescientist/) by [Hudson Smith](https://github.com/dhudsmith).

The prerequisites for using the program are listed in the `requirements.txt` file. Run `discrete_hamiltonian.py` to show a numerical simulation of
a wavepacket in a Harmonic Oscillator. The script `eigenstates_animation.py` displays eigenstates in various potentials, and `compare_with_analytic.py` compares
numerically computed energy eigenvalues of the Harmonic Oscillator and Infinite Square Well with their analytical versions. The file `self_contained_example.py` is meant to be a short, standalone example of finding the eigenvalues and eigenstates of the discrete Hamiltonian.

Thanks to [rafael-fuente](https://github.com/rafael-fuente) for giving the suggestion to use kron/kronsum instead of using for loops to construct the Hamiltonian.

## References:

Discretizing the Hamiltonian:
 - [Discretization of 1D continuous Hamiltonian](https://wiki.physics.udel.edu/phys824/Discretization_of_1D_continuous_Hamiltonian)

Using 2D Grids for higher dimensional discrete operators (credit to [rafael-fuente](https://github.com/rafael-fuente) for the suggestion):
 - [Kronecker sum of discrete Laplacians](https://en.wikipedia.org/wiki/Kronecker_sum_of_discrete_Laplacians)
 - [Scipy Kronecker product](https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.kron.html)

Using shift-invert mode to speed up the compution of finding eigenvalues and eigenvectors (thanks to [dhudsmith](https://github.com/dhudsmith) for the suggestion):
 - [Scipy Shift-invert mode](https://docs.scipy.org/doc/scipy/reference/tutorial/arpack.html#shift-invert-mode)

Discrete Laplacian stencils:
- [Wikipedia - Image Processing via operator discretization](https://en.wikipedia.org/wiki/Discrete_Laplace_operator#Implementation%20via%20operator%20discretization)

Energies for analytically solvable potentials (used to compare it with the numerical solutions):
- [N-dimensional Harmonic Oscillator](https://en.wikipedia.org/wiki/Quantum_harmonic_oscillator#N-dimensional_isotropic_harmonic_oscillator)
- [Infinite Square Well](https://en.wikipedia.org/wiki/Particle_in_a_box#Higher-dimensional_boxes)

Domain colouring using hue angle:
- [Wikipedia - Hue](https://en.wikipedia.org/wiki/Hue)
- [HSV-RGB Comparison](https://en.wikipedia.org/wiki/File:HSV-RGB-comparison.svg)

SPS-QM-2D

SPS-QM-2D 최신버젼 다운로드

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