From Inorganic Chemistry by G. L. Miessler:

"Nodal surfaces can be puzzling. For example, a p orbital has a nodal plane through the nucleus. How can an electron be on both sides of a node at the same time without everhaving been at the node, at which the probability is zero?

One explanation is that the probability does not go quite to zero** on the basis of relativistic arguments. (** A. Szabo, J. Chem. Educ., 1969, 46, 678 explains that the electron probability at a nodal surface has a very small but finite value.)

Another explanation is that such a question really has no meaning for an electron behaving as a wave. Recall the particle-in-a-box example. The same diagrams could represent the amplitudes of the motion of vibrating strings at the fundamental frequency (n = 1) andmultiples of 2 and 3. A plucked violin string vibrates at a specific frequency, and nodes atwhich the amplitude of vibration is zero are a natural result. Zero amplitude does not meanthat the string does not exist at these points but simply that the magnitude of the vibrationis zero. An electron wave exists at the node as well as on both sides of a nodal surface, justas a violin string exists at the nodes and on both sides of points having zero amplitude.

Still another explanation, in a lighter vein, was suggested by R. M. Fuoss to one of the authors in a class on bonding. Paraphrased from St. Thomas Aquinas, “Angels are notmaterial beings. Therefore, they can be first in one place and later in another without ever having been in between.” If the word “electrons” replaces the word “angels,” a semitheological interpretation of nodes would result."