*Alan Corney*

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780199211456
- eISBN:
- 9780191705915
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199211456.003.0003
- Subject:
- Physics, Atomic, Laser, and Optical Physics

This chapter derives the quantum mechanical wave functions which describe the energy levels of simple atoms. Schrödinger's equation is introduced as well and the angular part of the equation is ...
More

This chapter derives the quantum mechanical wave functions which describe the energy levels of simple atoms. Schrödinger's equation is introduced as well and the angular part of the equation is solved for spherically symmetric potentials. The orbital angular momentum operator is defined and the concept of intrinsic spin is introduced. The extension of these results to atoms with several electrons using the central-field approximation is introduced. Spectroscopic notation for Russell-Saunders coupling is discussed.Less

This chapter derives the quantum mechanical wave functions which describe the energy levels of simple atoms. Schrödinger's equation is introduced as well and the angular part of the equation is solved for spherically symmetric potentials. The orbital angular momentum operator is defined and the concept of intrinsic spin is introduced. The extension of these results to atoms with several electrons using the central-field approximation is introduced. Spectroscopic notation for Russell-Saunders coupling is discussed.

*C. Julian Chen*

- Published in print:
- 2007
- Published Online:
- September 2007
- ISBN:
- 9780199211500
- eISBN:
- 9780191705991
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199211500.003.0004
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter discusses the physics and properties of four types of atomic forces occurring in STM and AFM: the van der Waals force, the hard core repulsion, the ionic bond, and the covalent bond. The ...
More

This chapter discusses the physics and properties of four types of atomic forces occurring in STM and AFM: the van der Waals force, the hard core repulsion, the ionic bond, and the covalent bond. The general mathematical form of the van der Waals force between a tip and a flat sample is derived. The focus of this chapter is the covalent-bond force, which is a key in the understanding of STM and AFM. The concept of covalent bond is illustrated by the hydrogen molecular ion, the prototypical molecule used by Pauling to illustrate Heisenberg's concept of resonance. The Herring-Landau perturbation theory of the covalent bond, an analytical incarnation of the concept of resonance, is presented in great detail. It is then applied to molecules built from many-electron atoms, to show that the perturbation theory can be applied to practical systems to produce simple analytic results for measurable physical quantities with decent accuracy.Less

This chapter discusses the physics and properties of four types of atomic forces occurring in STM and AFM: the van der Waals force, the hard core repulsion, the ionic bond, and the covalent bond. The general mathematical form of the van der Waals force between a tip and a flat sample is derived. The focus of this chapter is the covalent-bond force, which is a key in the understanding of STM and AFM. The concept of covalent bond is illustrated by the hydrogen molecular ion, the prototypical molecule used by Pauling to illustrate Heisenberg's concept of resonance. The Herring-Landau perturbation theory of the covalent bond, an analytical incarnation of the concept of resonance, is presented in great detail. It is then applied to molecules built from many-electron atoms, to show that the perturbation theory can be applied to practical systems to produce simple analytic results for measurable physical quantities with decent accuracy.

*Alan Corney*

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780199211456
- eISBN:
- 9780191705915
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199211456.003.0005
- Subject:
- Physics, Atomic, Laser, and Optical Physics

The quantum-mechanical selection rules for electric dipole radiative transitions between atomic energy levels are derived, firstly for one-electron atoms without spin, and then including spin angular ...
More

The quantum-mechanical selection rules for electric dipole radiative transitions between atomic energy levels are derived, firstly for one-electron atoms without spin, and then including spin angular momentum. The discussion is extended to many-electron atoms and rules for L, S, and J quantum numbers are derived.Less

The quantum-mechanical selection rules for electric dipole radiative transitions between atomic energy levels are derived, firstly for one-electron atoms without spin, and then including spin angular momentum. The discussion is extended to many-electron atoms and rules for L, S, and J quantum numbers are derived.