The wave function of the Lyman-alpha photon. I: The wave function in the angular and linear momentum representations (Q1865892)

The photon, among the various fundamental particles, has always been of extreme importance from various points of view. The question of a wave function for the photon emitted in an atomic, molecular or nuclear transition has ever attracted much attention. Here the author has derived the wave function in the momentum representation for the photon emitted by a non-relativistic hydrogen atom, when the electron of the atom falls from the first excited state to the ground state. A generalization of Dirac's procedure to find out the eigenfunctions in resonance scattering is used. Exact solution of the two-level problem is obtained employing the exact matrix elements of interaction. After the introduction, the Hamiltonian of hydrogen atom interacting with photon field eigenfunctions of Hamiltonian and wave function of the Lyman-\(\alpha\) photon in the energy-angular momentum representation, examination of resonance and finally the linear momentum representation are treated in detail. The paper gives a very good understanding of the Lyman-alpha photon.