Schrodinger velocity operator

Differentiating the already established Schrodinger velocity operator from the last section with respect to time, we obtain... 

The paradox was elucidated through the trembling motion (Zillerbewegung) discovered by Schrodinger [8] while investigating the velocity operators cik introduced by Dirac to linearize his equation. The equation of motion of a velocity component, Vk = coik, can be written as... 

Of course, the explicit form of the velocity operator depends on H. For the Schrodinger Hamiltonian, Eq. (4.46), we obtain the Schrbdinger velocity operator... 

So far we have discussed nonrelativistic ab initio methods they ignore those consequences of Einstein s theory of relativity that are relevant to chemistry (section 4.2.3). These consequences arise in the special (rather than the general) theory, from the dependence of mass on velocity [4. This dependence causes the masses of the inner electrons of heavy atoms to be significantly greater than the electron rest mass since the Hamiltonian operator in the Schrodinger equation contains the electron mass (Eqs (5.36) and (5.37)), this change of mass should be taken into account. Relativistic effects in... 

Including also the next term of the expansion, Eq. (2.88), gives rise to additional operators including the mass-velocity, Darwin and one-electron spin-orbit operators, which can be used in perturbation theory calculations of relativistic corrections to the non-relativistic results of the Schrodinger equation and molecular properties. However, the expansion is based on the assumption that the scalar potential r) is small, which is not fulfilled for the inner electrons of heavy atoms, because close to the nucleus they are exposed to the strong Coulomb potential of the nucleus. For this situation the expansion is then no longer valid. Alternative expansions exist, which circumvent this... 

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