In quantum mechanics, a single photon is described by a probability wave or wave function. The behavior of this wave function determines the probability of finding the photon at different positions in space when it is measured.
The wave function of a photon can exhibit different spatial profiles depending on the specific circumstances. When a photon is emitted from a source, it typically spreads out in all directions, similar to a spherical wave. This is because the wave function of the photon extends through space, and the probability of finding the photon is non-zero in all directions around the source.
However, when considering the propagation of the photon over longer distances, the wave function can be approximated as a plane wave. This approximation is often used when analyzing the behavior of photons in experiments like the two-slit experiment or when studying their interactions with matter.
In the two-slit experiment, for example, a single photon can be thought of as a wave that passes through both slits simultaneously, creating an interference pattern on a screen behind the slits. This wave-like behavior is consistent with the idea that the photon's wave function spreads out in a plane perpendicular to the direction of motion.
It's important to note that while the wave function of a single photon can exhibit wave-like properties, the ultimate measurement or detection of the photon occurs at a specific location as a particle-like event. The wave function describes the probability distribution for finding the photon at different positions, but the actual outcome of measurement corresponds to a single point in space.
So, to summarize, while a single photon is described by a wave function that can exhibit wave-like behavior, it is not accurately represented by a classical electromagnetic wave. The behavior of photons is fundamentally quantum mechanical and exhibits both particle-like and wave-like characteristics.