Energy levels and radiative transitions

If the potential V is time-independent, wave functions satisfying the Schrodinger equation can be factored into a space function and one periodic in time. 

To find a time-dependent solution of the Schrodinger equation we apply perturbation theory. We assume that a transition between two energy levels is caused by a time-dependent influence, which we represent as a small additive potential, v x, y, z, t). The Schrodinger equation is then 

The time-dependent wave function, 4, can be expressed as a linear combination of the in Eq. (3.1.12). The integral 

To exanune the behavior during a transition, consider a molecule that is initially in state What is the probability of finding the molecule in another state if 2 at a later time t In a radiation field the molecule will be subjected to an oscillating electric field. 

E and Eo are vectors in jc, y, and z. The interaction energy is given by the scalar product of this field and the electric dipole moment, M, of the molecule. 

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Fig. 20. Diagram showmg energy levels and radiative transitions for the H-atom.

The spectra of these ions have not been interpreted experimentally but the Slater-Condon method was applied to the sequence As I — Ag XV for predicting energy levels and radiative transition probabilities within the ground configuration 4s 4p. Slater and spin-orbit parameters are from Hartree-Fock calculations, corrected for relativistic effects and scaled to fit the known elements [3]. The predicted levels are (energy in cm ) ... 

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