following factors: 1. Calculational ease: the delta function is the paradigm for time-dependent systems because one can proceed further in the analysis without recourse to drastic approximations; 2. Effects of chaos: since our primary objective is to explore the quantum manifestations of classical chaos, we are more interested in the general issues of chaos, rather than specific functional forms. Even for a more ‘physical’ choice of $f(t)=A\cos(\omega t)$, one can easily show that the resulting functional form of $\Omega^2(t)$ can be approximated sensibly as above; and 3. Classical considerations: as shown in the Appendix, starting from the Lorenz force plus Maxwell’s equations, one can write the classical equations of motion [*exactly*]{} including the self-induced fields, even for the magnetic field given by $B(t) = B_{dc} + B_{ac} T_0\sum_{n=-\infty}^{\infty} 
\delta (t-nT_0)$. Classically, the associated Lagrangian is linear in the vector potential. There are regularization problems, however, when using this form in the quantum Hamiltonian, since in this case there is an ill defined $A_{ac}^2(t)$ term present. However, the model $H=H_{dc}+H_1$ is well defined.

In order to more clearly see what the relevant parameters in the problem are, we go over to dimensionless units, defined by rescaling all lengths to the disk 