Quantum Optics for Engineers

14

Matrix Aspects of Quantum Mechanics

14.1  Introduction

As mentioned in Chapter 1, the Heisenberg matrix mechanics provides one of the three main avenues to quantum mechanics. This approach to quantum mechanics was disclosed in three papers authored by Heisenberg (1925), Born and Jordan (1925), and Born et al. (1926). An iconic result from the Heisenberg–Born–Jordan contribution was the commutation rule

$pq-qp=\frac{h}{2\text{π}i}$

(14.1)

or

$pq-qp=-i\hslash$

(14.2)

Here, we examine the origin of the commutation rule, using the Feynman approach, and provide a brief pragmatic introduction to some salient aspects of matrix quantum mechanics with a focus on Pauli matrices. We begin with a review preamble on vector and matrix algebra.

14.2  Introduction to ...