In quantum mechanics (QM) and quantum field theory (QFT), a particle state refers to the quantum description of a particle or a system of particles. It represents the state of the particle in terms of its observable properties, such as position, momentum, energy, and spin. The particle state is described by a mathematical object called a wave function or a state vector.
In QM, a particle state is represented by a wave function, which is a complex-valued function that evolves over time according to the Schrödinger equation. The wave function contains information about the probability amplitude for the particle to be found in different states upon measurement. The squared magnitude of the wave function gives the probability density distribution of finding the particle at different positions or with different properties.
In QFT, the concept of particle states is more nuanced due to the framework of quantum fields. In QFT, particles are described as excitations of quantum fields that permeate space. The quantum fields are operators that create or annihilate particles, and the state of the system is described by the occupation numbers of these particles in various modes of the field. The states in QFT are represented by Fock states, which are built upon the vacuum state.
One of the key differences between particle states in QM/QFT and classical states is the probabilistic nature of quantum states. In classical physics, the state of a system can be precisely determined, and its properties can be predicted with certainty. In contrast, quantum states are characterized by inherent uncertainty due to the principles of superposition and measurement in QM. A particle can exist in a superposition of different states until it is measured, at which point the wave function collapses to a specific outcome with a certain probability.
Another significant distinction is the concept of entanglement in quantum states, which is absent in classical states. In quantum systems, particles can become entangled, meaning the state of one particle is inherently connected to the state of another particle, even if they are spatially separated. This phenomenon has no classical counterpart and is a fundamental aspect of quantum mechanics.
Overall, particle states in QM and QFT are fundamentally different from classical states due to their probabilistic nature, the principles of superposition and measurement, and the presence of entanglement. These quantum concepts lead to a rich and distinct framework for describing the behavior of particles and systems at the microscopic level.