Transition probabilities of a Markov chain on energy levels

An electron can occupy one of a countable number of energy levels in atom. The transition probabilities from i’s to j’s level per second are given by

\[ P _ { i j } ( t = 1 ) = c _ { i } e ^ { - \alpha | i - j | } ,\tag{54} \]

where \(\alpha > 0\) and \(c _ { i }\) are some constants. Find

1. \(P _ { i j } ( t = 2 )\)

2. \(c _ { i } .\)