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Particle in a box - The particle in a box (or the infinite potential well) is a simple idealized system that is completely solved within quantum mechanics. The infinite potential well is a finite sized region in space (the box) with an infinite potential at its boundaries (the walls). A particle experiences no forces while inside the box, but as the walls are 'infinitely high', it is constrained to remain in the box.
Simple Harmonic Oscillator - One of the most important model system in quantum mechanics because a wide variety of physical situations can be reduced to it either exactly or approximately. In particular, a system near an equilibrium configuration can often be described in terms of one or more harmonic oscillators. Furthermore, it is one of the few quantum mechanical systems for which a simple exact solution is known.
Thanks to Mikhail Noginov and Vladimir Gavrilenko for helping with the theory.
Center for Materials Science, Norfolk State University.
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