Expectations, studying quantum mechanics

One of the purposes of this work is to make contact between relativistic corrections in quantum mechanics and the weakly relativistic limit of QED for this problem. In particular, we will check how performing plane-wave expectation values of the Breit hamiltonian in the Pauli approximation (only terms depending on c in atomic units) we obtain the proper semi-relativistic functional consistent in order ppl mc ), with the possibility of analyzing the separate contributions of terms with different physical meaning. Also the role of these terms compared to next order ones will be studied. 

Cytosine as well as the other heterocyclic nucleic acid bases are quasiaromatic compounds, expected to be planar. The experimental evidence shows that this is not strictly so, but the deviations of the ring atoms of cytosine from planarity are, in general, small, and in most cases within the limits of the experimental accuracy. Oxygen and amino groups, and the atoms of substituents, when present, appear to deviate more from planarity. In all the quantum-mechanical studies the cytosine ring has been assumed to be planar. 

Another important quantum mechanical problem of interest to nuclear chemists is the penetration of a one-dimensional potential barrier by a beam of particles. The results of solving this problem (and more complicated variations of the problem) will be used in our study of nuclear a decay and nuclear reactions. The situation is shown in Figure E.5. A beam of particles originating at — oo is incident on a barrier of thickness L and height V0 that extends from x = 0 to x = L. Each particle has a total energy E. (Classically, we would expect if E < V0, the particles would bounce off the barrier, whereas if E > V0, the particles would pass by the barrier... 

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