11.1: Magnetic Dipole Model

Most of the results below apply to the general multi-state model of a physical system implied by quantum mechanics; see Chapter 10. However, an important aspect is the dependence of energy on external parameters. For example, for the magnetic dipole, the external parameter is the magnetic field \(H\). Here is a brief review of the magnetic dipole so it can be used as an example below.

This model was introduced in section 9.1.2. Figure 11.1 shows a system with two dipoles and two environments for the system to interact with. (Of course any practical system will have many more than two dipoles, but the important ideas can be illustrated with only two.) The dipoles are subjected to an externally applied magnetic field \(H\), and therefore the energy of the system depends on the orientations of the dipoles and on the applied field. Each dipole, both in the system and in its two environments, can be either “up” or “down,” so there are four possible states for the system, “up-up,” “up-down,” “down-up,” and “down-down.” The energy of a dipole is \(m_dH\) if down and \(−m_dH\) if up, and the energy of each of the four states is the sum of the energies of the two dipoles.

Figure 11.1: Dipole moment example. Each dipole can be either up or down