PART I: Fundamentals

1

Basic Quantum Mechanics

1.1 MEASUREMENTS AND PROBABILITY

In the beginning of 20th century, it was discovered that the behavior of very small particles, such as electrons, the nuclei of atoms, and molecules, cannot be described by classical mechanics, which had been quite successful in explaining the macroscopic world until then. Nonetheless, it was soon discovered that the description of these phenomena on the atomic scale is possible by the set of laws described by quantum mechanics. Both classical mechanics and quantum mechanics are based on the description of measurements of observable quantities called dynamical variables, such as position, momentum, and energy. Consider an experiment in which we can make three measurements successive in time. Let’s denote the first of observable quantities A, the second B, and the third C. We also denote , and as one of a number of possible results that could come from the measurement of A, B, and C, respectively. Let be the conditional probability that if the measurement of A results in , then the measurement of B will result ...