Eigenstates in a sentence

A simple example of this is a free particle, whose energy eigenstates have wavefunctions that are propagating plane waves.

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.

Given that the eigenstates of an atom are properly diagonalized, the overlap of the wavefunctions between the excited state and the ground state of the atom is zero.

However, chirality of a massive particle is not a constant of motion; helicity is, but the chirality operator does not share eigenstates with the helicity operator.

However, since : the smallest eigen-number is 0, and : In this case, subsequent applications of the lowering operator will just produce zero kets, instead of additional energy eigenstates.

If one knows the corresponding wave function at the instant before the measurement, one will be able to compute the probability of the wave function collapsing into each of the possible eigenstates.

In physics, these standing waves are called " stationary states " or " energy eigenstates " in chemistry they are called " atomic orbitals " or " molecular orbitals ".

It may thus be utilized as an interaction term in a Hamiltonian, splitting the energy eigenvalues of its symmetric versus antisymmetric eigenstates.

More specifically, the energy eigenstates form a basis – any wavefunction may be written as a sum over the discrete energy states or an integral over continuous energy states, or more generally as an integral over a measure.

There are also objections to this theory based on what it says about particular situations usually involving eigenstates of an operator.

Therefore, it is helpful to use different words to describe states having uncertain values and states having definite values (eigenstates).

This density matrix formulation is not needed in cases of thermal equilibrium so long as the basis states are chosen to be energy eigenstates.

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.

To cope with this problem, Dirac introduced the hypothesis, known as hole theory, that the vacuum is the many-body quantum state in which all the negative-energy electron eigenstates are occupied.

While the occupation numbers are unchanged, nevertheless there is change in the energy levels of one-to-one corresponding, pre- and post-compression, eigenstates.