Ok, here's my take on this: A photon interacting with an electron
will always cause the electron to oscillate with the same frequency as the
photons E-field; we don't throw out everything we already know about E&M.
For an electron bound in an atom this oscillation is restricted bewteen
the available states. Take an example of two states, n and k. While
oscillating between the states, the electron, to a first approximation
appears as an oscillating dipole. Thus, we can describe what happens to
the electron by the expectation value of the dipole moment qr, where r is
the vector radial between the states. As the electron is really in *both*
states the total wavefunction is a linear superposition of Psi n, and Psi
k.
When one does the integral there is a time dependent term whose
frequency is exactly En-Ek/hbar times an integral of Psik* (r) Psin. So
whether a transition occurs boils down to what the value of that integral
is. Since (r) is odd, the parity of the integral is dependent only on the
product of the two wavefunctions. Their oddness or evenness is determined
by their values of l, and msubl.: hence we get the selection rules.
Now how do I translate this for a high school student??? What all
the above is really saying is that the photon *does* interact with the
electron, but the probability (there's that quantum word) is very samll
that the electron will make the jump if the two states are incompatible
(meaning violates selection rules). I think this is a great question, but
cannot be answered in the Bohr model framework. Unless one understands
the inherent probabilistic nature of QM it is very difficult to give an
answer that is going to be satisfying.