eigenstate


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eigenstate

[′ī·gən‚stāt]
(quantum mechanics)
A dynamical state whose state vector (or wave function) is an eigenvector (or eigenfunction) of an operator corresponding to a specified physical quantity.
References in periodicals archive ?
where | 0 > is the true electron vacuum, [[epsilon].sub.F] is the Fermi energy, and [c.sup.[dagger].sub.k([chi])[sigma]] creates an electron of spin [sigma] in the HF eigenstate with an eigenvalue [[epsilon].sub.k([chi])[sigma]] ([chi] = 1.2, ..., 12).
In [2] we applied this model on chain systems of harmonic quantum oscillators and could show that particle rest masses coincide with the eigenstates of the system.
For the present case, the conjecture indicated in [25], hereafter the (Knight) K-conjecture, is trivially verified since the number eigenstate |n> injected into the beam splitter to produce superposition (47) is clearly nonclassical if n [not equal to] 0.
Abram, "Eigenstate statistics and optical properties of one-dimensional disordered photonic crystals," Phys.
Exploiting this equivalence there is in principle no difference between manipulations in the spin space of neutrons with the orthogonal basis {|[up arrow]>, |[down arrow]>} as eigenstates of [[sigma].sub.z], and momentum space with {|k>, |k'>} as orthogonal basis vectors corresponding to two directions of the neutron beam in an interferometer.
Note that neither (2) nor (3) is an eigenstate for the location of the marble, and so neither can claim on that basis to be a state in which the marble has a determinate location.
6 as a movement of the quantum wave function to the left as L and the right as D) enters the consciousness of A: L or D becomes for A either a live or a dead cat, but for the ultimate observer, B, the joint state of the object-plusintermediate observer becomes a mixture [10] of the two joint eigenstates say [A.sub.L] x L and [A.sub.D] x D.
For it is a fundamental principle of orthodox Dirac-von Neumann quantum mechanics that an observable of a quantum system possesses a definite value at any particular time if and only if the quantum state of the system at that time is an eigenstate of the observable in question - a principle often called the eigenstate - eigenvalue link.
However, for t [greater than or equal to] 0 the particle state, which is no longer an energy eigenstate, is given by a superposition of the energy eigenstates [[psi].sub.k](x) (k = [square root of (E)]) of the potential [V.sub.2](x), i.e., [36]
WFC implies the apparent selection of one single eigenstate:
Table 1: Wootters discrete Wigner function for a few pure states [rho] = [absolute value of [psi]> <[psi]| State Eigenstate of [W.sub.[rho]] |0> [[sigma].sub.z] [mathematical expression not reproducible] 1/[square root of 2] [[sigma].sub.x] [mathematical (|0> + |2>) expression not reproducible] 1/[square root of 2] [[sigma].sub.y] [mathematical (|0> - i|2>) expression not reproducible] |H> H = [[sigma].sub.x] [mathematical + [[sigma].sub.z]/ expression not [square root of 2] reproducible] |T> SH [mathematical expression not reproducible] Table 2: The magic states p (column 2) and the sum of negative entries in the Wigner matrix [W.sub.[rho]] (column 3).
In the recent research about quantum sliding-mode control (SMC) [26,27], a sliding mode is defined based on the fidelity with a desired eigenstate, and the goal is to maintain the state in the mode or drive it back into the mode after measurement.