Properties of Wavefunctions

Fedor Herbut

Peter Joshua Atkins, Julio de Paula, James Keeler

This chapter examines the interpretation of the wavefunction, and specifically what it reveals about the location of a particle. In quantum mechanics, all the properties of a system are expressed in terms of a wavefunction, which is obtained by solving the equation proposed by Erwin Schrödinger. Indeed, wavefunctions provide the essential foundation for understanding the properties of electrons in atoms and molecules, and are central to explanations in chemistry. The chapter then considers how, according to the Born interpretation, the probability density at a point is proportional to the square of the wavefunction at that point. A wavefunction is normalized if the integral over all space of its square modulus is equal to 1. Ultimately, a wavefunction must be single-valued, continuous, not infinite over a finite region of space, and have a continuous slope. The quantization of energy stems from the constraints that an acceptable wavefunction must satisfy.

HU Kun-ming, 商丘师范学院物理与信息工程系，商丘 476000

The transformation property between the configuration wavefunction of the equivalent-electron and the Young tableau is pointed out to be unitary but not to be Hermite unitary. And a sign error of the spectrum item wavefunction is presented.