Based on the generalized Weyl quantization scheme, which relies on the generalized Wigner operator Ω k (p, q) with a real k parameter and can unify the P-Q, Q-P, and Weyl ordering of operators in k = 1, −1, 0, respectively, we find the mutual transformations between δ(p − P)δ(q − Q), δ(q − Q)δ(p − P), and Ω k (p, q) , which are, respectively, the integration kernels of the P-Q, Q-P, and generalized Weyl quantization schemes. The mutual transformations provide us with a new approach to deriving the Wigner function of quantum states. The P− and Q− ordered forms of Ω k (p, q) are also derived, which helps us to put the operators into their P− and Q− ordering, respectively.
Design of a new spiro-typed core structure is one of
the most important
approaches for developing highly efficient hole-transporting materials
(HTMs). In this work, the strategies of modifying with O/S heteroatoms
and introducing a helical π-linker are evaluated based on the
typical FDT molecule. Theoretical calculations show that all the highest
occupied molecular orbitals (HOMOs) and the lowest unoccupied molecular
orbitals (LUMOs) of the studied HTMs are matched well with the energy
band structure of perovskite, and the HOMO levels display a gradually
negative-shifted trend from the FDT to SM30, which means that the
favorable hole extraction and the easy interfacial energy regulation
can be anticipated. Compared to the light absorption of the FDT, the
absorption spectra of new tailored HTMs are slightly red-shifted.
More importantly, our results indicate that introducing a helical
π-linker and modification with heteroatoms in the spiro-typed
core can be the effective methods to promote the hole transport ability
of HTMs. Both the methods can effectually heighten the crystal stacking
and intermolecular electronic couplings and further facilitate the
hole transport of HTMs. Furthermore, the large Stokes shifts and the
better solubility are also displayed for the newly tailored HTMs.
In sum, this work provides useful insights for the design of highly
efficient HTMs, and three new spiro-typed HTMs are proposed.
The coherent-entangled state |α, x; λ> with real parameters λ is proposed in the two-mode Fock space, which exhibits the properties of both the coherent and entangled states. The completeness relation of |α, x; λ> is proved by virtue of the technique of integral within an ordered product of operators. The corresponding squeezing operator is derived, with its own squeezing properties. Furthermore, generalized P-representation in the coherent-entangled state is constructed. Finally, it is revealed that superposition of the coherent-entangled states may produce the EPR entangled state.bipartite coherent-entangled state, IWOP technique, classical transformation
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