The 2-norbornyl cation

The norbornyl cation, discussed in section 7.9 of Miller's Advanced Organic Chemistry, can be represented by either a classical or a non-classical structure:

classical non-classical
classical structure non-classical structure

These structures are NOT equivalent in any sense, and in fact they can both be optimized with quantum chemical calculations. The structures shown below are optimized at the ab initio 3-21G level, with the classical more stable than the non-classical by about 0.5 kcal/mol.

classical non-classical

The non-classical cation is, in fact, the transition state for the alkyl shift shown below:

bridge-shifting in the norbornyl cation