Zero-point energy

The zero-point energy is the difference between the energy possessed by a quantum-mechanical system in the ground state, and the energy minimum, which would have the system if you would describe it classic. In thermodynamic systems that exchange energy with their environment, the zero-point energy is thus equal to the energy of the system at absolute zero temperature.

The zero-point energy is not detectable by direct measurements, as these are only differences in energy capture. In quantum field theory, ie the sum of all zero energy vacuum energy since this energy plays the empty space with no particles. The vacuum energy can be demonstrated by means of the Casimir effect indirectly experimentally.

One-dimensional Einteilchensysteme

The zero point energy is usually introduced on the basis of one-dimensional systems of a particle in a potential. In the classical ( ie non- quantum ) physics is the lowest energy state in which the particle rests in the potential minimum. In quantum mechanics, the smallest achievable energy can exceed the value of the potential minimum. For example given systems, this can be verified by explicit determination of the energy eigenstates. Alternatively, you can obtain this result by using the uncertainty principle: A finite position uncertainty, for example, present in bound states, generally requires a pulse of focus greater than zero. Therefore, the impulse and the kinetic energy can not be exactly zero. Since the kinetic energy can not be negative, the energy must be the sum of the potential energy and kinetic energy, to be thus larger than the minimum potential energy.

Harmonic Oscillator

The standard example for the zero-point energy is the quantum mechanical harmonic oscillator. This has the potential, so a potential minimum, and the power spectrum

Where the reduced Planck constant and the angular frequency of the oscillator respectively. Even in the lowest energy state, the ground state, thus there exists a non-zero energy.

In the classical case of the lowest energy state is that in which the particles resting at the location, that is. In quantum mechanics, however, prohibits the uncertainty relation between position and momentum that both variables have exact values ​​. The more accurate the location is known, the less accurate one knows the pulse, and vice versa. Clearly there is the zero-point energy as the average of these fluctuations.