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Coupled Harmonic Oscillator Lattice Eigenmodes
Plot of eigenvectors (mode configurations) and eigenvalues (mode frequencies) for a classical lattice of coupled harmonic oscillators, with open, closed, and periodic boundary conditions. These were generated from harmonic-lattice.py. A full description of the Lagrangian is commented in the code.
In these plots, each eigenvector is plotted with its eigenvalue given by x-axis height (the same way, eg, that particle in a box modes are often depicted).
Caution: If you click, get ready to SCROLL a LOT!
And here is an example (different params) of the eigenvalues coalescing as BCs transition from closed to periodic.
Various states of a quantum simple harmonic oscillator, shown in both position and number bases. (Note: missing mag squared signs in annotation text of image.)
Induced Probability Density on Qubit Subsystems
The file below shows some properties of a qubit embedded within a higher dimensional pure subsystem.