eigenstates's Usage Examples:

Hence, starting from one eigenstate of the unperturbed Hamiltonian H_0, the state of the system oscillates between the eigenstates of H_0 with a frequency (known as Rabi frequency),From the expression of P_{21}(t) we can infer that oscillation will exist only if \left| W_{12} \right|^2 \ne 0.

There are two complications with neutral kaons: Due to neutral kaon mixing, the K0 S and K0 L are not eigenstates of strangeness.

At this very low temperature, vibrational energy in the ion trap is quantized into phonons by the energy eigenstates of the ion strand, which are called the center of mass vibrational modes.

much like classical objects, as illustrated in the figure; they are not eigenstates of the Hamiltonian.

old eigenstates into the new ones.

its energy levels and eigenstates) can be expressed as "corrections" to those of the simple system.

The normalized eigenstates corresponding to \mu_L and \mu_H respectively, in the natural basis \left\{ \left| P \right\rangle, \left| \bar{P} \right\rangle \right\} \equiv \left\{\left(1, 0\right), \left(0, 1\right) \right\} are,p and q are the mixing terms.

Non-stationary wave functions are linear combinations of the eigenstates of the system.

For the eigenstates of charge conjugation, C | ψ ⟩ η C | ψ ⟩ {\displaystyle {\mathcal {C}}\.

) and a very weak coupling between the third (that is, the third does not affect the interaction between the other two), equation () gives the probability of a neutrino of type \alpha transmuting into type \beta as,P_{\beta\alpha} \left( t \right) \sin^2\theta \sin^2\left( \frac{E_+ - E_-}{2\hbar}t \right)where, E_+ and E_- are energy eigenstates.

Description as a two-state system A special case: considering mixing only Caution: mixing here does not refer to quantum mixed states, but rather to the pure state superposition of energy (mass) eigenstates that is described by a so-called mixing matrix.

We can switch between these states using the CKM matrix for the quarks, or the PMNS matrix for the neutrinos (the charged leptons on the other hand are eigenstates of both mass and flavour).

quantum states that exhibit coherence between eigenstates of certain observables.