I understand a wave involving lots of particles as with water molecules. One particle disturbs or imparts energy to the particle next to it and so on. But how does a single electron or photon impart energy to itself?
Maybe this will help. Maybe.
Water waves, waves on a vibrating string, sound, and light are all waves (classically). Yet they are all very different things. Different things are moving, different media (or maybe no medium in the case of light). The motion of the moving bits can be parallel (sound) or perpendicular (water) with respect to the motion of the wave.
When physicists look at these problems generally, the similarity we see is in the equations that govern their motion, which is called the
wave equation, which has certain mathematical features.
When quantum mechanics was developed, it became clear that the motion of quantum wavicles obeyed something that looks quite a lot like the wave equation. The Schrödinger wave equation describes the motion of our wavicles, which are mathematically represented by a 'wavefunction'.
If you like, it is the similarity to the wave equation that leads us to name the probability function the wave function. And because of the mathematical similarities, the behavior of these objects is similar to what we think of as classical waves.
ETA: But wavicles are
not waves in the sense of a disturbance caused by bits of matter jiggling the bits of matter next to them.
Quoting the wiki page on the
Schrödinger equation:
The nonrelativistic Schrödinger equation is a type of partial differential equation called a wave equation. Therefore it is often said particles can exhibit behavior usually attributed to waves.
In most modern interpretations this description is reversed – the quantum state, i.e. wave, is the only genuine physical reality, and under the appropriate conditions it can show features of particle-like behavior.
Two-slit diffraction is a famous example of the strange behaviors that waves regularly display, that are not intuitively associated with particles. The overlapping waves from the two slits cancel each other out in some locations, and reinforce each other in other locations, causing a complex pattern to emerge. Intuitively, one would not expect this pattern from firing a single particle at the slits, because the particle should pass through one slit or the other, not a complex overlap of both.
However, since the Schrödinger equation is a wave equation, a single particle fired through a double-slit does show this same pattern (figure on right). Note: The experiment must be repeated many times for the complex pattern to emerge. The appearance of the pattern proves that each electron passes through both slits simultaneously.[7][8][9] Although this is counterintuitive, the prediction is correct; in particular, electron diffraction and neutron diffraction are well understood and widely used in science and engineering.
Related to diffraction, particles also display superposition and interference.
The superposition property allows the particle to be in a quantum superposition of two or more states with different classical properties at the same time. For example, a particle can have several different energies at the same time, and can be in several different locations at the same time. In the above example, a particle can pass through two slits at the same time. This superposition is still a single quantum state, as shown by the interference effects, even though that conflicts with classical intuition.
