The scattering of particles, which is described by collision theory in Newtonian mechanics, undergoes significant changes when examined through the lens of quantum mechanics. Quantum mechanics introduces the wave-particle duality, uncertainty principle, and the concept of wavefunctions, which fundamentally alter our understanding of particle interactions.
In Newtonian mechanics, particles are considered classical objects with definite positions and momenta. The collision theory describes their interactions based on well-defined trajectories and classical laws of motion. The outcome of a collision can be determined by analyzing the initial conditions and the forces involved.
However, in quantum mechanics, particles are described by wavefunctions that exhibit probabilistic behavior. The wavefunction represents the probability amplitude distribution of a particle and encodes information about its position, momentum, and other properties. When particles interact, their wavefunctions combine and evolve according to the laws of quantum mechanics.
The scattering of particles in quantum mechanics is typically described using quantum scattering theory. Unlike classical mechanics, the position and momentum of particles are not simultaneously well-defined due to the uncertainty principle. Instead, we consider the probabilities of different scattering outcomes.
Quantum scattering theory calculates scattering cross-sections, which provide information about the probability of a particular scattering event occurring. It takes into account the incident particles' wavefunctions, the potential energy field they encounter, and the interaction between them. The wavefunctions are usually described using mathematical equations such as the Schrödinger equation or the scattering matrix formalism.
Quantum mechanics introduces phenomena like wave interference and quantum tunneling, which have no classical analogues. These effects can lead to surprising scattering behavior, such as the diffraction of particles or the possibility of particles passing through potential barriers that would be classically forbidden.
Additionally, quantum mechanics allows for the description of composite particles, such as atoms or molecules, which have internal structure and additional degrees of freedom. These internal states can influence the scattering process, leading to phenomena like resonances or inelastic scattering.
In summary, the scattering of particles described by collision theory in Newtonian mechanics is significantly modified under the framework of quantum mechanics. Quantum scattering theory incorporates probabilistic wavefunctions, wave-particle duality, uncertainty principles, wave interference, quantum tunneling, and the internal structure of particles to provide a more accurate and comprehensive description of scattering phenomena.