Chapter 8

The problems of this chapter are focused on measurement probability.

Background material

In quantum theory the mathematics that describes the observation of a physical occuring event (process) is only provided probabilistically. This means that the physical system in the quantum state $|\Phi\rangle$ can actually be discussed as having a probability of being in a quantum state $|\Psi\rangle$, this is given as:

If $|\Phi\rangle = |\Psi\rangle$, then its the probability of being is a specific quantum state $|\Psi\rangle$. The outcome for a measurement, more specifically a measurement operator corresponding to an observable in some state $\psi$, has a probability:

where $i$ corresponds to a specific measurment outcome, for example, spin-up or spin-down of an electron. Because something had to happen during the outcome of applying a measurment operator or equally saying "observing a measurement", the set of outcomes – our spin-up and spin-down for example – requires that they form a complete set. This is represented by the completeness equation:

where $\mathbf{I}$ is the identity. In the example of spin-up and spin-down particles the two operators in matrix form are:

Problems

Programing Problems

• Problem 1

• Problem 2