When a particle enters an excited state, the energy appears in its quantum wavefunction according to $E = h \nu$.
Does the $E$ in this equation also include kinetic energy, and rest mass energy? Or are they "held" somewhere else? Or are kinetic/mass energy a different framework for looking at the same phenomenon, and if so how do they relate?
Also, if the particle gathers enough excitation energy to escape a potential well, and therefore escapes that well, from which 'budget' is the necessary energy taken - kinetic, frequency or mass; and why?