A derivation of a more general expression, called the " m "-dependent LeRoy radius, which depends on the magnetic quantum number ( " m " ), was derived in 1995.
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The quantum numbers article ( http : / / en . wikipedia . org / wiki / Quantum _ numbers ) says that the magnetic quantum number should be between the negative and positive values of the azimuthal quantum number.
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The azimuthal quantum number is the second of a set of quantum numbers which describe the unique quantum state of an electron ( the others being the principal quantum number, following spectroscopic notation, the magnetic quantum number, and the spin quantum number ).
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For example, when dealing with the energy spectrum of the electron in a hydrogen atom, the relevant state vectors are identified by the principal quantum number, the angular momentum quantum number, the magnetic quantum number, and the spin z-component.
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Each orbital in an atom is characterized by a unique set of values of the three quantum numbers,, and, which respectively correspond to the electron's energy, angular momentum, and an angular momentum vector component ( the magnetic quantum number ).
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And " m " is called the magnetic quantum number, because the " z " component of the angular momentum is the magnetic moment of the rotator along the " z " direction in the case where the particle at the end of the rotator is charged.
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However, the observed fine structure when the electron is observed along one axis, such as the " z "-axis, is quantized in terms of a magnetic quantum number, which can be viewed as a quantization of a vector component of this total angular momentum, which can have only the values of "' " } }.
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Where " P " " m " is an associated Legendre polynomial, is the orbital angular momentum quantum number, and " m " is the orbital magnetic quantum number which takes the values ", " + 1, . . . " 1, The formalism of spherical harmonics have wide applications in applied mathematics, and are closely related to the formalism of spherical tensors, as shown below.
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