Degenerate energy levels

Summary

In quantum mechanics, an energy level is degenerate if it corresponds to two or more different measurable states of a quantum system. Conversely, two or more different states of a quantum mechanical system are said to be degenerate if they give the same value of energy upon measurement. The number of different states corresponding to a particular energy level is known as the degree of degeneracy (or simply the degeneracy) of the level. It is represented mathematically by the Hamiltonian for the system having more than one linearly independent eigenstate with the same energy eigenvalue. When this is the case, energy alone is not enough to characterize what state the system is in, and other quantum numbers are needed to characterize the exact state when distinction is desired. In classical mechanics, this can be understood in terms of different possible trajectories corresponding to the same energy. Degeneracy plays a fundamental role in quantum statistical mechanics. For an N

Official source

https://en.wikipedia.org/wiki/Degenerate_energy_levels

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A Novel Method to Quantify Self-Healing Capabilities of Fiber-Reinforced Polymers

Amaël Maximilien Cohades, Véronique Michaud, Cecilia Scazzoli, Robin Samuel Trigueira

The present work investigates a novel and practical method to evaluate the healing efficiency of carbon-reinforced polymer composites. The method should be representative of damage occurring during the lifetime of a composite part, should tend to damage the healable matrix mostly and yet be simple and cost-effective to set up. Thus, the capacity to recover low-velocity impact damage has been evaluated via three-point bending flexural tests. Carbon-reinforced composite laminates were produced using HealTech (TM) T300-TW200-42RW-1250, a commercially healable resin pre-impregnated Torayca T300 3K twill 2 x 2 fabric with an aerial weight of 200 g/m(2). Fibers were oriented at +/- 45 degrees or at 0 degrees-90 degrees, and the laminates were impacted at different energy levels. Flexural properties of undamaged, damaged, and healed samples were compared, and the healing efficiency was calculated as the ratio of healed and undamaged ultimate flexural strength or modulus. Since matrix healing efficiency is the value to characterize, it was shown that +/- 45 degrees laminates could be tested without major fiber damage and, thus, provide the best matrix healing efficiency results. Such a method proved to be 1) representative of early-stage damage of composite FRPs often occurring in the form of delamination or matrix microcracking, and 2) a fast and reliable characterization technique requiring the use of a limited amount of material.

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