ABSTRACT
This chapter outlines the formal rules of quantum mechanics. A formal mathematical object that possesses these properties was introduced by Dirac and called the Dirac delta function. It is discussed further in Appendix C. The association of wave functions with vectors is actually more than a mere analogy. It is possible to formulate quantum mechanics abstractly in the language of generalized vectors and to regard wave functions as simply one particular representation of the vector algebra. The chapter discusses that the wave functions that arise from the standard physical problems to be considered do form a complete set. In quantum mechanics one frequently deals with infinite-dimensional space and the question of completeness is mathematically delicate. In classical mechanics there is a well-known association between the existence of geometrical symmetries in a mechanical system and the constancy in time of certain dynamical quantities.
