The First Two Postulates of Quantum Mechanics

The Schrodinger equation does not provide a complete theory of quantum mechanics. Schrodinger, Heisenberg, and others devised several postulates (unproved fundamental assumptions) that form a consistent logical foundation for nonrelativistic quantum mechanics. In any theory based on postulates, the validity of the postulates is tested by comparing the consequences of the postulates with experimental fact. The postulates of quantum mechanics do pass this test. These postulates can be stated in slightly different ways. We will state five postulates in a form similar to that of Mandl and Levine. The first two postulates were introduced in Chapter 15 without calling them postulates. We now state them explicitly  

Postulate 1. All information that can be obtained about the state of a mechanical system is contained in a wave function, which is a continuous, finite, and single-valued function of time and of the coordinates of the particles of the system. 

This postulate implies that there is a one-to-one relationship between the state of the system and a wave function. That is, each possible state corresponds to one wave function, and each possible wave function corresponds to one state. The terms state function and wave function sre often used interchangeably. Information about values of mechanical variables such as energy and momentum must be obtained from the wave function, instead of from values of coordinates and velocities as in classical mechanics. The fourth postulate will provide the method for obtaining this information. 

PostulatG 2. The wave function I obeys the time-dependent Schrodinger equation 

The time-independent Schrodinger equation can be derived from the time-dependent equation, as was shown in Chapter 15, by assuming that the wave function is a product of a coordinate factor and a time factor  

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