In quantum mechanics, particles can exhibit wave-like behavior, including particles that are in a stationary state. This wave-particle duality is a fundamental concept in quantum mechanics and is described by wave functions.
A stationary particle in quantum mechanics refers to a particle that is in an eigenstate of its Hamiltonian, which means its energy is well-defined and does not change over time. For example, an electron in a bound state around an atomic nucleus can be in a stationary state with a specific energy level.
Even though the particle is stationary in the sense that its position does not change over time, its wave function can still exhibit wave-like properties. The wave function of a stationary particle is a standing wave, which means it oscillates in space but does not propagate.
The behavior of the wave function is described by the Schrödinger equation, which is a fundamental equation in quantum mechanics. The wave function of a stationary particle satisfies the Schrödinger equation with a time-independent potential, resulting in a wave function that is a solution to the equation for a specific energy level.
The wave-like behavior of the stationary particle is reflected in various phenomena. For instance, the wave function can exhibit interference and diffraction effects, similar to waves. In experiments such as the double-slit experiment, even stationary particles can show interference patterns, indicating their wave-like nature.
It is important to note that while particles in quantum mechanics can exhibit wave-like behavior, they also possess particle-like properties, such as localized interactions and discrete energy levels. The wave-particle duality is a fundamental aspect of quantum mechanics, and it is through this duality that the behavior of particles is described.