STATE VECTOR

The state vectors defined previously can also be called ket vectors or kets. The overall spin state of an electron can be expressed as one of the ket of the Z-component of the spin operator, or as linear

FIGURE 1: A schematic showing different quantum states.

superposition of the two or more kets as shown:

.........(1)

......(2)

where c_↑ and c_↓ are complex numbers. If we have a ket |xl corresponding to an observable ˆx, that can take on all values in a certain range (“x” is continuous variable), the state vector can be expressed as an integral:

We will show later how to obtain the previous expression. For simplicity, the focus will be limited to discrete variables, such as spin vectors corresponding to 2D vector space (discrete variables) to better understand the mathematical foundation. Later, more complex, generalized systems will be explored.