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单词 degenerate
释义
degenerate

Mathematics
  • Where a family of entities can be defined in terms of parameters, and the limiting case produces an entity which is of a different nature. For example, the general quadratic function is in the form y = α‎x2 + β‎x + γ‎, and the graph is a parabola. As α‎ decreases the curvature of the parabola steadily decreases, and the limiting case as α‎ → 0 is a straight line, which is a degenerate parabola.


Chemistry
  • Having quantum states with the same energy. For example, the five d-orbitals in an isolated transition-metal atom have the same energy (although they have different spatial arrangements) and are thus degenerate. The application of a magnetic or electric field may cause the quantum states to have different energies (see crystal-field theory). In this case, the degeneracy is said to be ‘lifted’.


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