Wave Packets and Teleconnections

Abstract

In this chapter, we discuss another aspect of the wave packet theory, wave packet progagation. Earlier chapters mainly focused on the structure and structural change of wave packets, without explicit discussions of the propagation property of wave packets, which is possible only when the structure independence theorem discussed in Chapter 2 holds. However, when the structure independence theorem is not valid, we have to take the propagation property of the wave packet into account, as discussed in Chapter 2. Moreover, the propagation property of wave packet is also of great importance. As shown in Chapter 2, the wave packet is always propagated along the group velocity, that is, the wave packet velocity. Many modern ideas on wave propagation were originated by Rayleigh, including the distinction between the phase velocity and the group velocity; this appears very early in Rayleigh’s work (1877). Since then, there have been numerous studies on wave packet propagation associated with the group velocity, including several monographs (Brillouin, 1946, 1953, 1960; Tolstoy, 1973). The study of wave packet propagation was started as soon as the concept of wave group or wave packet was introduced in wave mechanics (Brillouin, 1946).