Quantum mechanics is the branch of physics that studies the behavior of matter and energy in the presence of an observer. It is the foundation of modern physics and the theory of wave-particle duality.
In classical mechanics, particles are point-like objects that follow well-defined trajectories in space and time. In quantum mechanics, particles are described by a wave function that encodes all possible information about their behavior. The wave function is a mathematical description of a particle, not a physical entity itself.
The wave function evolves according to the Schrödinger equation, which is a differential equation that describes how waves propagate through space and time. The Schrödinger equation depends on the potential energy of the system, which determines the allowed states of motion for the particles.
The solutions to the Schrödinger equation are called eigenfunctions or eigenstates. Each eigenstate corresponds to a particular state of motion for the particles in the system. The wave function can be expanded as a superposition of eigenfunctions, which allows it to describe any state of motion for the particles.
Particles in quantum mechanics do not have definite positions or momenta; instead, they have probability distributions for these quantities. The position and momentum distributions are related by Heisenberg’s uncertainty principle, which states that certain pairs of physical properties cannot both be known with arbitrary precision. For example, if we know exactly where a particle is located, we cannot say anything about its momentum except that it has some uncertainty associated with it. Conversely, if we know exactly what its momentum is, we cannot say anything about its position except that it has some uncertainty associated with it. This tradeoff between position and momentum is known as Heisenberg’s uncertainty principle