Atomic, molecular, and optical physics electron is treated quantum mechanically. In low speed collisions the approximation fails. Classical Monte-Carlo methods for the dynamics of electrons can be described as semi-classical in that the initial conditions are calculated using a fully quantum treatment, but all further treatment is classical. Atomic, Molecular and Optical physics frequently considers atoms and molecules in isolation. Atomic models will consist of a single nucleus that may be surrounded by one or more bound electrons, whilst molecular models are typically concerned with molecular hydrogen and its molecular hydrogen ion. It is concerned with processes such as ionization, above threshold ionization and excitation
Theoretical and experimental justification for the Schrödinger equation the clock in the observer frame. A wave-like picture of particles is thus consistent with special relativity. In fact, we now know that these relations can be succinctly written using special relativistic 4-vector notation: The relevant four-vectors are: The relations between the four-vectors are as follows: The phase of the wave is the relativistic invariant: The de Broglie hypothesis helped resolve outstanding issues in atomic physics. Classical physics was unable to explain the observed behaviour of electrons in atoms. Specifically, accelerating electrons emit electromagnetic radiation according to the Larmor formula. Electrons orbiting a nucleus should lose energy to radiation and