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  2. Orbitals with the same energy

    Orbitals with the same energy are called degenerate. (In other contexts, degenerate means immoral, or other bad things.) In general, the more complications you add, like more electrons, neighboring atoms, magnetic fields, etc, the fewer orbitals are degenerate. So for a hydrogen atom by itself, all the orbitals in each shell are degenerate.
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    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 … See more

    The possible states of a quantum mechanical system may be treated mathematically as abstract vectors in a separable, complex Hilbert space, while the See more

    If two operators $${\displaystyle {\hat {A}}}$$ and $${\displaystyle {\hat {B}}}$$ commute, i.e., $${\displaystyle [{\hat {A}},{\hat {B}}]=0}$$, … See more

    Degeneracies in a quantum system can be systematic or accidental in nature.
    Systematic or essential degeneracy
    This is also called a … See more

    The degeneracy in a quantum mechanical system may be removed if the underlying symmetry is broken by an external perturbation. … See more

    This section intends to illustrate the existence of degenerate energy levels in quantum systems studied in different dimensions. The … See more

    The physical origin of degeneracy in a quantum-mechanical system is often the presence of some symmetry in the system. Studying the symmetry of a quantum system can, in … See more

    The hydrogen atom
    In atomic physics, the bound states of an electron in a hydrogen atom show us useful examples of … See more

     
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