Non-relativistic Schrodinger equation

As the basis set becomes infinitely flexible, full Cl approaches the exact solution of the time-independent, non-relativistic Schrodinger equation. 

Hol0IEN, E., Proc. Phys. Soc. A71, 357, "The 2s2 XS state solution of the non-relativistic Schrodinger equation for He and H. " Associated Laguerre functions. 

The solution of the time independent, non-relativistic Schrodinger equation has the potential to solve all our problems. Knowledge of the geometry of the molecule, allows the calculation of the wavefunction and energy of the molecule, from the deceptively simple equation ... 

It is interesting to note that the Coulomb matrix and the matrix of the nuclear potential present in Vc are opposite in sign. This means that an underestimation, or complete neglect, of the Coulomb matrix will lead to a larger Vc and thus to an overestimation of the relativistic effect. If Vc is negligable compared to 2c the ZORA equation reduces to the non relativistic Schrodinger equation. 

Note that the non-relativistic Schrodinger equation is recovered when w s set to 1. 

Beyond the Molecular Orbital Approach Introduction.—In principle an exact solution to the non-relativistic Schrodinger equations for a molecule can be achieved by the configuration interaction technique. A complete set of one-electron spin orbitals i is used to form a complete set of Slater determinants by choosing all possible ordered sets of n elements of the set of 4u s. A linear combination of these determinants is then used ... 

In table 2 our result is compared with the UV spectroscopic result of Klein et al. [26], Also shown are the theoretical results of Zhang et al. [2], Plante et al. [27], and Chen et al. [28], The first of these uses perturbation theory, with matrix elements of effective operators derived from the Bethe-Salpeter equation, evaluated with high precision solutions of the non-relativistic Schrodinger equation. This yields a power series in a and In a. The calculations of Zhang et al. include terms up to O(o5 hi a) but omit terms of 0(ary) a.u. The calculations of Plante et al. use an all orders relativistic perturbation theory method, while those of Chen et al. use relativistic configuration interaction theory. These both obtain all structure terms, up to (Za)4 a.u., and use explicit QED corrections from Drake [29],... 

The Born Oppcnheimer electronic Hamiltonian was given previously in (6.77) and a method of obtaining exact solutions is described in appendix 6.1. If the Bom expansion (6.131) is substituted into the complete non-relativistic Schrodinger equation, using the Hamiltonian (6. 130), we obtain a set of coupled differential equations for the functions... 

Rigorous solution of the non-relativistic Schrodinger equation in the Born-Oppen-heimer approximation... 

The non-relativistic Schrodinger equation for a confined hydrogen-like atom 205... 

The aim of modern quantum chemistry is, simply stated, to apply the rigorous principles of quantum mechanics to molecular systems in order to gain useful insight into chemical phenomena. The starting point for most such quantum mechanical investigations is the time-independent non-relativistic Schrodinger equation ... 

The attempt to correct the non-relativistic Schrodinger equation in an approximate way for relativistic effects leads to the appearance of an one-electron operator, known as electron-nucleus Darwin term [109],... 

It s relation to the non-relativistic Schrodinger-equation can be shown using the relation... 

Consider first the case where A = 0. We then recover the non-relativistic Schrodinger equation... 

To treat relativistic effects theoretically, the Dirac equation is usually solved rather than the non-relativistic Schrodinger equation. The one-electron Dirac Hamiltonian is written by... 

Dirac showed in 1928 that a fourth quantum number associated with intrinsic angular momentum appears in a relativistic treatment of the free electron, it is customary to treat spin heuristically. In general, the wavefunction of an electron is written as the product of the usual spatial part (which corresponds to a solution of the non-relativistic Schrodinger equation and involves only the Cartesian coordinates of the particle) and a spin part a, where a is either a or p. A common shorthand notation is often used, whereby... 

The basis of the use of quantum mechanics is that we can construct a total molecular wave function using which a time independent non-relativistic Schrodinger equation of the form. 

For many applications an adequate description of a one-electron atom is obtained by combining a wavefunction obtained from the non-relativistic Schrodinger equation with one of the spin functions a or jS to give... 

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