Atomic Units - Use and Notation

Use and Notation

Atomic units, like SI units, have a unit of mass, a unit of length, and so on. However, the use and notation is somewhat different from SI.

Suppose some particle has a mass m which is 3.4 times the mass of electron. Then, the value of m can be written in three ways:

• "". This is the clearest notation (but least common), where the atomic unit is included explicitly as a symbol.
• "" ("a.u." means "expressed in atomic units"). This notation is ambiguous: Here, it means that the mass m is 3.4 times the atomic unit of mass. But if a length L were 3.4 times the atomic unit of length, the equation would look the same, "" The dimension needs to be inferred from context.
• "". This notation is similar to the previous one, and has the same dimensional ambiguity. It comes from formally setting the atomic units to 1, in this case, so .