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We note that the following discussion is restricted to non-degenerate eigenstates, which is the natural situation in large quantum systems [43] and also applies to the situation studied in this paper.
These polynomials are necessary for constructing Gaussian quadrature formulas that are encountered in large quantum chemistry computational packages and in calculating the Compton scattering kernel and its associated angular moments.
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Second, there is the intensity interpretation according to which it is a statistical agreement in the limit of large quantum numbers between the quantum intensity, understood in terms of the probability of a quantum transition, and the classical intensity, understood as the square of the amplitude of one component of the classical motion.
Strictly speaking this intensity correspondence is exact only in the limit of large quantum numbers, and cannot be extended to small quantum numbers.
Alternatively, the behavior of a quantum model should reproduce the behavior of macroscopic classical models in the limit of large quantum numbers.
Note that this equality between the quantum frequency and one component of the classical frequency only holds in the limit of large quantum numbers not for low quantum-number transitions.
First, there is the frequency interpretation, according to which the correspondence principle is a statistical asymptotic agreement between one component in the Fourier decomposition of the classical frequency and the quantum frequency in the limit of large quantum numbers.
The spectral lines are built up by a whole ensemble of atoms undergoing transitions between different stationary states, and these spectral lines, though they exhibit a pattern of regularity, are not evenly spaced except in the limit of large quantum numbers.
This states that the behaviour of systems described by quantum theory reproduces classical physics in the limit of large quantum numbers.
This strongly supports the occurrence of large quantum effects proposed in a recent theoretical study.
Our proposal can be extended to achieve QIT between any two selected NVCEs in a large hybrid system by adjusting system parameters, which is important in large scale quantum information processing.
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