 If formula_27 is an infinitesimal real quantity formula_28, then the unitary transformation is very close to the identity matrix (the final state is very close to the initial state) and can be written

and the adjoint by

The factor of i is introduced for convenience.With this convention, it will be shown that energy conservation requires H to be a Hermitian operator and that H is related to the energy of a particle.Energy conservation requires

Since formula_32 is infinitesimal, which means that formula_33 may be neglected
with respect to formula_32, the last term can be omitted.