1. Consider a PIB with length a
Consider a PIB with length a. The system is described by some wave function , which can be written in terms of the PIB eigenstates j (i.e., the EFs of the Hamiltonian) as a basis, where the j are the EFs of the PIB.
Measuring the energy of ONE system yields ...
... E = n2h2/8ma2, with some arbitrary n.
... E = n2h2/8ma2, always with the same n.
(C) ... E = n2h2/8ma2, with some n, depending on the cj.

2. Consider a PIB with length a
Consider a PIB with length a. The system is described by some wave function , which can be written in terms of the PIB eigenstates j (i.e., the EFs of the Hamiltonian) as a basis, where the j are the EFs of the PIB.
Measuring the energy of ONE system yields ...
... E = n2h2/8ma2, with some arbitrary n.
... E = n2h2/8ma2, always with the same n.
(C) ... E = n2h2/8ma2, with some n, depending on the cj.