In the case of two subsystems, one factor is a wave function satisfying a regular schrdinger equation, while the other factor is a conditional

probability amplitude satisfying a more complicated schrdinger-like equation with a non-local, non-linear and non-hermitian hamiltonian .

The data generated from these measurements were used to plot cumulative

probability amplitude and interevent interval graphs, with each distribution normalized to a maximal value of one.

The wave function is a complex-valued

probability amplitude, and the probabilities for the possible results of measurements made on the system can be derived from it.

In the table, [[alpha].sub.1] and [[beta].sub.1] are the

probability amplitude of global optimal solution, [d.sub.1] = [[alpha].sub.1] x [[beta].su.1] and [[xi].sub.1] = [tan.sup.-1]([[beta].sub.1]/[[alpha].sub.1]); [[alpha].sub.2] and [[beta].sub.2] are the

probability amplitude of current solution, [d.sub.2] = [[alpha].sub.2]2 x [[beta].sub.2] and [[xi].sub.2] = [tan.sup.-1]([[beta].sub.2]/[[alpha].sub.2]).

where [alpha], [beta] are tow complex of

probability amplitude of the corresponding state, where [[absolute value of a].sup.2] + [[absolute value of b].sup.2] = 1 ([[absolute value of a].sup.2] and [[absolute value of b].sup.2] represent the occurrence probabilities of qubit in the states of |0> and |1>, respectively).

Quantum genetic algorithm applies the

probability amplitude of qubits to encode chromosome and uses quantum rotating gates to realize chromosomal updated operation.

Here [u.sub.p](t) and stand for the excited-state and groundstate

probability amplitudes of the qubit with the vacuum state of the PhC reservoir while [C.sub.[??]](t) is the

probability amplitude of the photonic state at fc.

The essence of the Feynman path integral approach to quantum mechanics is in the

probability amplitude (also known as the propagator or the Green function) K([x.sub.b], [t.sub.b]; [x.sub.a], [t.sub.a]) for a particle starting from a position [x.sub.a] at time [t.sub.a] to reach a position [x.sub.b] at a later time [t.sub.b], which arises from the contributions from all trajectories from [x.sub.a] to [x.sub.b]:

A (quaternionic)

probability amplitude distribution that is attached to the current granule of a given chain takes care of the fact that the chain in the neighborhood of the current granule stays sufficiently smooth.

In a word, it has the phase sifted

probability amplitude of -1/[N.sup.1/2].

Here the quantity p[e.sup.i[pi][alpha]] can be called the complex

probability amplitude. It characterises two parameters of the random variable distribution, namely, the expectation value itself, [e.sup.i[pi][alpha]], and the probability density, p, i.e.

[Technically, a classical probability is measured with a positive real number; a quantum "

probability amplitude" is measured with a complex number; the collapsed final probability is the magnitude of this number squared, a real, positive number.]