interactions, quantum states, motion in the quantum world
Fig. 1. Energies and wavefunctions of the electron in a simplified one-dimensional valley, physicists call it a potential, which confines the electrons motion similarly as it is confined to the atomic volume, when it is bound to the nucleus. (© bf)
Quantum electrodynamics is the theory describing the states of electrons
and photons. According to this theory, photons mediate the force acting between charged particles and exerted on them by electromagnetic waves. This mediation occurs by the absorption and emission of photons. To a good approximation, these interactions can also be described in terms of electromagnetic forces, unless the interacting light is so weak that it is transported in isolated photons.
and photons. According to this theory, photons mediate the force acting between charged particles and exerted on them by electromagnetic waves. This mediation occurs by the absorption and emission of photons. To a good approximation, these interactions can also be described in terms of electromagnetic forces, unless the interacting light is so weak that it is transported in isolated photons.Electrons, just like photons, exhibit also a wave-like nature. This can only be accounted for by quantum theory and comes to light whenever electrons interact with structures comparable to or smaller than the wavelength of the electron, see box. This is the case whenever electrons are bound to atomic structures. The quantum state of the electron is given by a wavefunction, which is a number varying in space and time, like in a wave. The square of this number gives the probability with which the electron can be found at different positions around the nucleus of the atom. This probability distribution, which we shall simply refer to as an “electron cloud” is all we can say about its position.
In a quantum state of definite energy, this distribution does not change in time, i.e. the electron is at rest. Therefore we call such a state a stationary state. If the electron is – with some probability – in two (or more) stationary states simultaneously, i.e. its wavefunction is the sum (superposition) of the wavefunctions of the individual stationary states, its propability distribution becomes time dependent. Hence the electron is set into motion. The larger the energy difference between the participating states, the faster the motion, see box. The energies of loosely-bound electrons (far from the nucleus) differ by a fraction of an electronvolt, whereas the energy levels of strongly-bound states (near the atomic core) are separated as much as tens to thousands of electronvolts. Correspondingly, the time scale of electron motion inside atoms ranges from femtoseconds to attoseconds.
, whereas the energy levels of strongly-bound states (near the atomic core) are separated as much as tens to thousands of electronvolts. Correspondingly, the time scale of electron motion inside atoms ranges from femtoseconds to attoseconds.
The wavefunction of a free electron is a plane wave, with a
wavelength of
, m_e is the electron’s rest mass and v its velocity. It is also referred to as De Broglie wavelength, named after the discoverer of the wave-like nature of electrons.
If the electron occupies, with some probability, two bound, stationary quantum states of energy W_1 and W_2, its probability distribution oscillates with f, proportional to the energy difference, \Delta W = W_2 - W_1, between the two states:
\lambda_e = h/m_e\,v,
where h is Planck’s constant, m_e is the electron’s rest mass and v its velocity. It is also referred to as De Broglie wavelength, named after the discoverer of the wave-like nature of electrons.
If the electron occupies, with some probability, two bound, stationary quantum states of energy W_1 and W_2, its probability distribution oscillates with f, proportional to the energy difference, \Delta W = W_2 - W_1, between the two states:
f = \Delta W / h,
where h is Planck’s constant. Hence, the period, T_{\rm osc}, i.e. rapidity of the motion is given by
T_{\rm osc} = 1/f = h/\Delta W.