Chapter 4. Wave Mechanics

P. J. E. Peebles

Patrick A. Heelan

Anthony Duncan A, Michel Janssen B

Abstract This chapter explores Schrödinger’s introduction of wave mechanics. After briefly covering Schrödinger’s earlier work, it turns to the investigations that led him to write a four-part paper in 1926 introducing and applying wave mechanics. The chapter provides a detailed analysis of these four papers, in which the analogy of the new theory to the Hamilton-Jacobi formulation of classical mechanics plays a central role, as well as the paper written in between the second and the third installment on the relation between wave and matrix mechanics. The chapter also discusses Schr "odinger’s original interpretation of his wave functions and the reception of his theory by the physics community.

Louis Harris, Arthur L. Loeb, Peter B. Kahn

Caio Lima Firme

In this chapter shows some applications of matrix and wave mechnanics. The equivalence between matrix mechanics and wave mechanics is explored in this chapter. Another approach for this equivalence is indicated as well. The Heisenberg equation of motion is applied to the quantum virial theorem and quantum theory of atoms in molecules (QTAIM) in next section. It is introduced afterwards that the Heisenberg’s matrix mechanics is applied to the helium atom leads to the concept of quantum resonance and chemical bond. Next, the use of the matrix mechanics and wave mechanics to obtain the uncertainty principle is discussed and its derivation is also given. Subsequently, Dirac’s quantum mechanics – an amalgamation of matrix mechanics and wave mechanics – is introduced. Finally, the importance of the commutation of the quantum operators to the quantum mechanics is discussed followed by some basic quantum principles from the Copenhagen interpretation. A couple of examples and exercises is also available in this chapter.(156 words).

A.L. Stanford, J.M. Tanner