On the relation between Schrödinger and von Neumann equations

The relation between the density matrix obeying the von Neumann equation and the wave function obeying the Schrödinger equation is discussed in connection with the superposition principle of quantum states. The definition of the ray-addition law is given, and its relation to the addition law of vectors in the Hilbert space of states and the role of a constant phase factor of the wave function is elucidated. The superposition law of density matrices, Wigner functions, and tomographic probabilities describing quantum states in the probability representation of quantum mechanics is studied. Examples of spin-1/2 and Schrödinger-cat states of the harmonic oscillator are discussed. The connection of the addition law with the entanglement problem is considered.     

Ligand-Mediated Revival of Degraded α-CsPbI3 to Stable Highly Luminescent Perovskite

Although α-CsPbI₃ is regarded as an attractive optical luminophore, it is readily degraded to the optically inactive δ-phase under ambient conditions. Here, we present a simple approach to revive degraded (“optically sick”) α-CsPbI₃ through “medication” with thiol-containing ligands. The effect of different types of thiols is systematically studied through optical spectroscopy. The structural reconstruction of degraded α-CsPbI₃ nanocrystals to cubic crystals in the presence of thiol-containing ligands is visualized through high-resolution transmission electron microscopy and supported by X-ray diffraction analysis. We found that 1-dodecanethiol (DSH) effectively revives degraded CsPbI₃ and results in high immunity towards moisture and oxygen, hitherto unreported. DSH facilitates the passivation of surface defects and etching of degraded Cs₄PbI₆ phase, thus reverting them back to the cubic CsPbI₃ phase, leading to enhanced PL and environmental stability.