The principal quantum number, denoted as \( n \), is a fundamental quantum number used in quantum mechanics to describe the energy levels of electrons in an atom. It provides information about the size and energy of an electron's orbital. Here are some key points about the principal quantum number: 1. **Definition**: The principal quantum number indicates the main energy level (or shell) occupied by an electron.
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For a hydrogenic bound state, the principal quantum number is the positive integer that determines the unperturbed energy. Its allowed orbital quantum numbers are .
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Determines energy. This comes out directly from the resolution of the Schrödinger equation solution for the hydrogen atom where we have to set some arbitrary values of energy by separation of variables just like we have to set some arbitrary numbers when solving partial differential equations with the Fourier series. We then just happen to see that only certain integer values are possible to satisfy the equations.