By John Lowe (Auth.)

ISBN-10: 0124575528

ISBN-13: 9780124575523

This article starts off with a six-chapter advent of normal one-dimensional platforms, the hydrogen atom, many-electron atoms, and ideas of quantum mechanics. It then appears at edition and perturbation equipment, staff thought, Huckel and prolonged Huckel equipment, qualitative MO conception, and MO idea of periodic platforms

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**Sample text**

The kind of energy level splitting just described is an extremely pervasive phenomenon in quantum chemistry. When two atoms interact to form a molecule, the original atomic wavefunctions combine to form molecular wavefunctions in much the same way as was just described. One of these molecular wavefunctions may have an energy markedly lower than those in the corre sponding atoms. Electrons having such a wavefunction will stabilize the mole cule relative to the separated atoms. Another case in which energy level splitting occurs is in the ammonia molecule.

QUANTUM MECHANICS OF SOME SIMPLE SYSTEMS situation, the symmetry proof of Section 2-2 does not hold. However, there will always be an independent pair of degenerate wavefunctions that will satisfy certain symmetry requirements. Thus, in the problem at hand, we have one pair of solutions, the exponentials, which do have the proper symmetry since their absolute squares are constant. From this pair we can produce any number of linear combinations [one set being given by Eq. (2-41)], but these need not display the symmetry properties anymore.

Thus, an alternative set of solutions is ф = (1/V2^) exp( ± Щ\ k = 0, 1, 2, 3 , . . (2-51) The energies for the particle in the ring are easily obtained from Eq. (2-47): E = k2h2IS7T2I, k = 0, 1, 2, 3 , . . (2-52) The energies increase with the square of k, just as in the case of the infinite square well potential. Here we have a single state with E = 0, and doubly degenerate states above, whereas, in the square well, we had no solution at E = 0, and all solutions were nondegenerate. The solution at E = 0 means that there is no finite zero point energy to be associated with free rotation, and this is in accord with uncertainty principle arguments since there is no constraint in the coordinate ф.

### Quantum Chemistry Student Edition by John Lowe (Auth.)

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