# Basic state

The basic state of a quantum mechanical or quantum field theoretical system is its state with the lowest possible energy (see also energy level ).

When the only electron of the hydrogen atom can no longer give off any energy, it is in the ground state (bottom line)

## Quantum mechanics

The basic state of a system is always stable, since there is no state of lower energy into which it could pass ( decay ). A system in a state of higher energy (an excited state ) can, in accordance with the law of conservation of energy , pass into its basic state or a less highly excited state, if this is not prevented by certain laws, such as other laws of conservation ( selection rules ).

However, the term system is somewhat arbitrary. You can z. For example, consider the particles into which a radioactive atomic nucleus decays (e.g. nitrogen-14 nucleus + electron + antineutrino) as just another state of the original system (here carbon-14 nucleus); in this sense, the basic state of a radionuclide is not stable either.

The basic state of a quantum mechanical system does not have to be unique. If there are several states with the same lowest energy, this is called a degenerate ground state. One example is the spontaneous breaking of symmetry , where the symmetry of the system is reduced by the degeneracy of the ground state .

Since the temperature is a monotonically increasing function of the energy of the individual particles, systems in a "cold" environment are usually in their ground state. For most systems, e.g. B. Atoms , room temperature is already a cold environment.

A system in its ground state can still contain a surprising amount of energy. This can be seen in the example of the Fermi distribution of conduction electrons in a metal: the Fermi temperature of  the most energetic electrons near the Fermi edge is a few 10,000 K - even if the metal has cooled down well below room temperature. However, this energy cannot be extracted from the metal and used because the electron gas can not adopt an even lower energy state. ${\ displaystyle T_ {f} \! \,}$

## Quantum field theory

In quantum field theory , the ground state is often referred to as vacuum state , vacuum or quantum vacuum . The ground state on the flat Minkowski space-time is defined by its invariance under Poincaré transformations, in particular under time translation. Since the Poincaré group is not a symmetry group for curved spacetime , quantum fields in curved spacetime have i. General no clear ground state. To be more precise, there is only a unique ground state if there is a one-parameter isometric group of time translations of space-time.

## literature

• Peter W. Milonni: The quantum vacuum - an introduction to quantum electrodynamics. Acad. Press, San Diego 1994, ISBN 0-12-498080-5