Hamiltonian gauge transformed

This distinction is largely formal, owing to the substantial identity of the unitary time-dependent transformation (8)-(9) with the gauge transformations of the Hamiltonian and its eigenfunctions [21-22]. However, alterna-... 

In principle, a chemical shift calculation represents a perturbation theory, because of the presence of an external field Bz and magnetic moments due to the dipole character of nuclei. Therefore, perturbations to the Hamiltonian and the wave function have to be considered. The next important point is that the origin of the vector potential Az is not fixed due to the relation Bz = rot Az- Any change of the gauge origin Rq should not change any measurable observable. Therefore, a gauge transformation of the wave function 1%) and Hamilton operator h is essential... 

As long as ) differs from 4>) by more than a gauge transformation the state 4> ) represents some kind of excited state of the Hamiltonian with potential Vfi. The renormalized energy es associated with <> ) in the unprimed system is given by... 

The superconductor Hamiltonian (Eq. 21) is invariant under the following gauge transformation ... 

Similarly, form invariance of the time-independent Schrodinger equation under a gauge transformation is guaranteed by the simultaneous gauge transformation of the total Hamiltonian... 

Then, two things (that are actually interdependent) happen (1) The field intensity F = 0, (2) There exists a unique gauge g(R) and, since F = 0, any apparent field in the Hamiltonian can be transformed away by introducing a new gauge. If, however, condition (1) does not hold, that is, the electronic Hilbert space is truncated, then F is in general not zero within the tmncated set. In this event, the fields A and F cannot be nullified by a new gauge and the resulting YM field is true and irremovable. 

In the Hamiltonian conventionally used for derivations of molecular magnetic properties, the applied fields are represented by electromagnetic vector and scalar potentials [1,20] and if desired, canonical transformations are invoked to change the magnetic gauge origin and/or to introduce electric and magnetic fields explicitly into the Hamiltonian, see e.g. refs. [1,20,21]. Here we take as our point of departure the multipolar Hamiltonian derived in ref. [22] without recourse to vector and scalar potentials. 

Ferraro and coll, used canonical transformation of the Hamiltonian to resolve the average optical rotatory power of a molecule into atomic contributions, based on the acceleration gauge for the electric dipole, and/or the torque formalism [151], This method has been applied to the study of the conformational profile of the optical rotatory poser of hydrogen peroxide and hydrazine [152]. 

Given this approximation, we can transform the Hamiltonian of Eq. (1.44) from the velocity gauge to the so-called length gauge in which the matter-radiation interaction term contains only the dot product of the dipole moment and the electric field. In order to do so we choose x [Eq. (1.5)] as... 

---