Quantum mechanics is the description of the behavior of matter and light on an atomic scale. Between 1926 and 1927 Schrödinger, Heisenberg, Born, and Pauli developed a consistent description of the behavior of matter on a small scale. The following postulates summarize this description.

I. Wavefunction Postulates (Schrödinger)

1. The dynamical state of a system of n particles is completely defined by a wavefunction
   Y(r₁,r₂ ,...,r_n;t) = Y(r;t).

2. The wavefunction evolves in time and space according to the time dependent Schrödinger equation.
   HY(r;t) = i dY(r;t)/dt

II. Operator Postulates (Born)

1. The probability of finding a particle in the volume element dV is given by the square of the wavefunction.
   Y*(r;t) Y(r;t) dV

2. For every observable property of the system, their corresponds a linear Hermitian operator.
   O

3. The possible results of a single measurement of a physical observable associated with an operator O is given by its eigen values. o_n
   O j_n = o_n j_n

4. The average value of a large number of observations of a given state Y(r;t) is given by the expectation value of the operator.
   <O> = < Y(r;t) |O| Y(r;t)>

III. Spin Postulates (Dirac and Pauli)

1. Electrons posses an internal degree of freedom with properties analogous to angular momentum whose z component assumes only two values +/2 or -/2.

2. Systems made up of many electrons are represented by a wavefunction that is antisymmetric to the interchange of electron coordinates.
   Y(r₁,r₂, ...,r_n;t) = -Y(r₂,r₁, ...,r_n;t)