We use the Lewis and Riesenfeld invariant method to obtain the exact Schrödinger wave functions for a time-dependent harmonic oscillator with and without an inverse quadratic potential. As a particular case we also obtain the wave functions for the Caldirola-Kanai oscillator.

Raman scattering is used to investigate the room temperature phonons of tetragonal $(I4∕m)$ ${\mathrm{Sr}}_2\mathrm{Co}\mathrm{W}{\mathrm{O}}_6$ and monoclinic $(P{2}_1∕n)$ ${\mathrm{Ca}}_2\mathrm{Co}\mathrm{W}{\mathrm{O}}_6$ , ${\mathrm{Sr}}_2\mathrm{Co}\mathrm{Te}{\mathrm{O}}_6$ , and ${\mathrm{Ca}}_2\mathrm{Co}\mathrm{Te}{\mathrm{O}}_6$ double perovskites. Both tetragonal and monoclinic structures result from small distortions of the $Fm\overline{3}m$ cubic lattice. Therefore, phonons were assigned according to correlations with those observed in the prototype $A_2{B}^{\prime }{B}^{″}{\mathrm{O}}_6$ $Fm\overline{3}m$ cubic structure and the internal vibrational modes of the oxygen octahedra. The observed shifts of some vibrations in the $A_2\mathrm{Co}B{\mathrm{O}}_6$ compounds upon changing either $A$ or $B$ elements are tentatively explained.

Polarized Raman spectroscopy has been used to obtain the room-temperature phonon spectra of the series of rare earth orthovanadate single crystals: $\mathrm{Sm}\mathrm{V}{\mathrm{O}}_4$ , $\mathrm{Ho}\mathrm{V}{\mathrm{O}}_4$ , $\mathrm{Yb}\mathrm{V}{\mathrm{O}}_4$ , and $\mathrm{Lu}\mathrm{V}{\mathrm{O}}_4$ . The observed Raman frequencies follow the overall mode distribution expected for ${\mathrm{REVO}}_4$ compounds with the tetragonal zircon structure. The variation of the mode frequency with atomic number across the lanthanide orthovanadate series was investigated, and the trend exhibited by the internal modes was explained by considering the force constants of $\mathrm{V}{\mathrm{O}}_4$ tetrahedron.

In this paper I have drawn out the steps to be followed in order to derive the exact Schrödinger wave function for a particle in a general one-dimensional time-dependent linear potential. To this end I have used the so-called Lewis and Riesenfeld invariant method, which is based on finding an exact quantum-mechanical invariant in whose eigenstates the exact quantum states are found. In particular, I have obtained the wave functions of a particle in the linear potential well, driven by a monochromatic electric field.