Operators and Wave Functions

Iwo Białynicki‐Birula

This chapter describes the photon wave function, and explains the basic properties of a well-defined mathematical object—a six-component function of space-time variables—that describes the quantum state of the photon. The most essential property that does not hold for the photon wave function is that the argument of the wave function cannot be directly associated with the position operator of the photon. The position operator for the photon simply does not exist. However, one should remember that for massive particles also, the true position operator exists only in the nonrelativistic approximation. The concept of localization associated with the Newton-Wigner position operator is not relativistically invariant. The photon wave function is not restricted to the wave mechanics of photons. The same wave functions also appear as mode functions in the expansion of the electromagnetic field operators.

John Snygg

The relationship between the density operator and operator solutions of Schr\"odinger's equation is discussed. We designate operator solutions of Schr\"odinger's equation as "operator wave functions" and show how they can be constructed from ordinary wave functions.

Robert B. Griffiths

Cao Li-ping

Structure about spin operator and spin wave function of electron have been discussed in the Sz representation by use of matrix representation about operator and wave function of mechanical quantity. Some interesting character are also found out and proved.