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The results obtained here allow giving a definite answer to this question, because in the infrared range, absorption can also have the nature of electronic transitions between states with the main quantum number equal to 2. The alpha-helix is interesting as a mathematical object too.
Subscript f of the energy ε f points to the standard set of quantum numbers: f = {n f, l f, m f }, where n f = 1, 2, 3, … is the main quantum number, which belongs to the set f, l f = 0, 1, 2, …, n f − 1 is the orbital quantum number, while m f = 0, ± 1, ± 2, …, ± l f is the azimuthal quantum number of the same set.
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In 1925, however, two Dutch physicists, Samuel Goudsmit and George Uhlenbeck, realized that, in order to explain fully the spectra of light emitted by the atoms of alkali metals, such as sodium, which have one outer valence electron beyond the main core, there must be a fourth quantum number that can take only two values, −1/2 and +1/2.
Here, p is the radial quantum number.
There is a magnetic quantum number also associated with the angular momentum of the quantum state.
So, that's the second quantum number.
The quantum number n labels the shell of the atom.
The next quantum number needed to specify an orbital is denoted l and called the orbital angular momentum quantum number.
Schulz, H. Phase diagrams and correlation exponents for quantum spin chains of arbitrary spin quantum number.
It required the introduction of a fourth quantum number, a highly counterintuitive move as the new quantum number represents nothing that can be visualised.
The number l, called the orbital quantum number, must be less than the principal quantum number n, which corresponds to a "shell" of electrons.
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