In quantum mechanics, particles can exhibit wave-like behavior, even when they are stationary. This is a fundamental aspect of wave-particle duality. The wave-like behavior is described by the particle's wavefunction, a mathematical function that characterizes the probability distribution of finding the particle in different states.
When a particle is in a stationary state, it means that its wavefunction does not change with time. In other words, the probability distribution for finding the particle in different positions remains constant. This stationary state is often associated with the particle being in an energy eigenstate, which is a state with a definite energy.
Even in a stationary state, the wavefunction can still exhibit wave-like properties. For example, it can undergo interference, where different parts of the wavefunction combine and interfere constructively or destructively, leading to patterns of constructive or destructive interference. This interference behavior is characteristic of waves.
An important example of stationary wave-like behavior is the standing wave, which is a wave that appears to be "stationary" due to the constructive and destructive interference of waves traveling in opposite directions. Standing waves are commonly observed in systems such as vibrating strings, where the ends are fixed and the waves reflect back on themselves.
In the quantum realm, similar standing wave patterns can arise in stationary states of particles, such as electrons in an atom or particles confined within a potential well. These standing wave patterns, known as wavefunctions, describe the probability distribution of finding the particle in different locations.
So, even though a stationary particle may not be physically moving, its wavefunction can exhibit wave-like properties and can show patterns of interference, similar to what we observe in waves.