Eigenstate in a sentence

Usually, a system will not be in an eigenstate of the observable (particle) we are interested in. However, if one measures the observable, the wave function will instantaneously be an eigenstate (or "generalized" eigenstate) of that observable.

Applying an annihilation operator followed by its corresponding creation operator returns the number of particles in the k th single-particle eigenstate: : The combination of operators is known as the number operator for the k th eigenstate.

Each eigenstate of an observable corresponds to an eigenvector of the operator, and the associated eigenvalue corresponds to the value of the observable in that eigenstate.

This also has the effect of turning a position eigenstate (which can be thought of as an infinitely sharp wave packet) into a broadened wave packet that no longer represents a (definite, certain) position eigenstate.

As a result of this interaction, the "stationary state" of the atom is no longer a true eigenstate of the combined system of the atom plus electromagnetic field.

Dirac further reasoned that if the negative-energy eigenstates are incompletely filled, each unoccupied eigenstate – called a hole – would behave like a positively charged particle.

For example, if a measurement of an observable A is performed, then the system is in a particular eigenstate Ψ of that observable.

For example, the free particle in the previous example will usually have a wave function that is a wave packet centered around some mean position x 0 (neither an eigenstate of position nor of momentum).

However, one can measure the position (alone) of a moving free particle, creating an eigenstate of position with a wave function that is very large (a Dirac delta ) at a particular position x, and zero everywhere else.

If the particle is in an eigenstate of position, then its momentum is completely unknown.

On the other hand, if the particle is in an eigenstate of momentum, then its position is completely unknown.

Therefore, any eigenstate of the electron in the hydrogen atom is described fully by four quantum numbers.

This means that the state is not a momentum eigenstate, however, but rather it can be represented as a sum of multiple momentum basis eigenstates.

We will now extend the discussion to continuous observables, such as the position x. Recall that an eigenstate of a continuous observable represents an infinitesimal range of values of the observable, not a single value as with discrete observables.

When a state is measured, it is projected onto an eigenstate in the basis of the relevant observable.

When that device makes a measurement, the wave function of the systems is said to collapse, or irreversibly reduce to an eigenstate of the observable that is registered.