Solution to 1986 Problem 99

The general formula for the binding energies of two oppositely charged objects orbiting each other with charges Z_1 e and -Z_2 e and masses m_1 e and m_2 e are
\begin{align*}E_n = \frac{-Z_1^2 Z_2^2 e^4 \mu}{2 \hbar^2 (4 \pi \epsilon_0)^2 n^2}\end{align*}
where \mu = (m_1 + m_2)/(m_1 m_2) is the reduced mass of the pair. In this case, Z_1 = Z_2 = 1 and m_1 = m_2 = m_e, so \mu = m_e/2. So, the energies for postronium are equal to the energies of the hydrogen atom divided by two.

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