# eigenstate

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## ei·gen·state

(ī′gən-stāt′)
n.
One of a set of quantum-mechanical descriptions of the possible state of a physical system, using the mathematics of eigenvectors and generally existing in a state of superposition until the moment of observation.

[eigen- (as in eigenvalue) + state.]
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A spin-bond-order-wave (SBOW) state is characterized by unequal canonical ensemble averages of the bond-centered up- and down-spin densities, [<[c.sub.n:A(i)+][c.sub.n':A'(i')]>.sub.HF] [not equal to] [<[c.sup.[dagger].sub.n:A(i)-][c.sub.n':A'(i')-]>.sub.HF], where [<...>.sub.HF] means taking the quantum average in a HF eigenstate. They are mathematically interesting but of no occurrence under any realistic parameterization .
In  we have proposed a new interpretation of the cosmic microwave background as a stable eigenstate in a chain system of oscillating protons.
As an immediate application consider the number eigenstate [[??].sub.n] = |n><n|, then
, the threshold level of disorder below which the probability of formation of an eigenstate at the center of a PBG is negligible was established.
Berry  was the first who addressed this issue in quantum mechanics: He considered a system initially in an eigenstate |n(R(t))>[.sub.t=0] of the governing Hamiltonian H(R(t)) dependent on the parameters R(t) changing with time t.
To this end, von Neumann proposed that the linear dynamics does not always apply; exactly when a measurement is performed on a system, the state of that system evolves nonlinearly and instantaneously to an eigenstate of the observable being measured (von Neumann , V.1).
This is because the vacuum |0> is not the eigen state of [T.sub.00], but the eigenstate of Hamiltonian H = [integral] [T.sub.00][d.sup.3]x (for the detailed discussions, see ).
In case where [absolute value of ([alpha])] = [absolute value of ([beta])]= 1/[square root]2 we see that the pure input state is an eigenstate of Cy.
It follows that any macroscopic apparatus designed to measure any observable of any microscopic object will almost certainly get into an entangled quantum state with that object that is not an eigenstate of the pointer observable of the apparatus.
In , for t < 0, the particle is in an eigenstate of a semi-infinite square-well potential [V.sub.1](x),
Wave function collapse (WFC) is the phenomenon whereby a wave function, representing a quantum system and thus expressed in the linear sum of its eigenstate basis, appears to single out one eigenstate thus reducing the otherwise linear supposition into one single term.
This definition follows from [20, Corollary 1] which establishes that any single-qubit pure state not one of the six Pauli eigenstates, together with Clifford group operations and Pauli eigenstate preparation and measurement, allows universal quantum computation.

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