The Essentials of Quantum Mechanics

This is the same as the condition hψ|ψi = 1, i.e., the state |ψi must be

normalized, or be a unit vector in Hilbert space. A state vector that does not

have unit norm can be normalized by dividing it by its norm.

The first axiom of quantum mechanics is a statement that embodies all

this.

Exercise 3.1. Normalize the vectors

“

1

1

#

and

“

1

−1

#

. Show that they are

orthogonal.

Exercise 3.2. Normalize the state |0i − 2i|1i.