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Published online by Cambridge University Press: 11 May 2023
According to the postulates of quantum mechanics, the state of a system is associated with a wave function that contains any measurable information on the system at any time. In this chapter we become familiar with wave functions and how they represent the position of particles within the system. Within the realm of quantum mechanics, the position of particles is not deterministic. It is defined by a probability distribution. The wave function is a position-dependent complex-valued amplitude, whose absolute value squared is identified with the probability density for locating the particle in the position space. This identification of the wave function with a probability amplitude imposes some limitation. Particularly, for a closed system in which the particles are bound, the wave function must be proper (square integrable) and normalizable. These properties are discussed and demonstrated for different coordinate systems.
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