New Exactly and Conditionally Exactly Solvable N-Body Problems in One Dimension

We study a class of Calogero-Sutherland type one dimensional N-body quantum mechanical systems, with potentials given by $$V( x_1, x_2, \cdots x_N) = \sum_{i <j} {g \over {(x_i - x_j)^2}} - \frac{g^{\prime}}{\sum_{i<j}(x_i - x_j)^2} + U(\sqrt{\sum_{i<j}(x_i - x_j)^2}),$$ where $U(\sqrt{\sum_{i<j}(x_i - x_j)^2})$'s are of specific form. It is shown that, only for a few choices of $U$, the eigenvalue problems can be solved {\it exactly}, for arbitrary $g^{\prime}$. The eigen spectra of these Hamiltonians, when $g^{\prime} \ne 0$, are non-degenerate and the scattering phase shifts are found to be energy dependent. It is further pointed out that, the eigenvalue problems are amenable to solution for wider choices of $U$, if $g^{\prime}$ is conveniently fixed. These conditionally exactly solvable problems also do not exhibit energy degeneracy and the scattering phase shifts can be computed {\it only} for a specific partial wave.Comment: 10 pages, latex, no figure

Synthesis of N-methyl-6-heterocyclic-1-oxoisoindoline derivatives by microwave assisted buchwald-hartwig amination

An rapid and efficient microwave assisted Pd(II) catalyzed protocol for the preparation of N-methyl-6-heterocyclic-1-oxoisoindoline derivatives by Buchwald-Hartwig amination with an overall yield 68-85% has been described

Quantum information entropies of the eigenstates and the coherent state of the P\"oschl-Teller potential

The position and momentum space information entropies, of the ground state of the P\"oschl-Teller potential, are exactly evaluated and are found to satisfy the bound, obtained by Beckner, Bialynicki-Birula and Mycielski. These entropies for the first excited state, for different strengths of the potential well, are then numerically obtained. Interesting features of the entropy densities, owing their origin to the excited nature of the wave functions, are graphically demonstrated. We then compute the position space entropies of the coherent state of the P\"oschl-Teller potential, which is known to show revival and fractional revival. Time evolution of the coherent state reveals many interesting patterns in the space-time flow of information entropy.Comment: Revtex4, 11 pages, 11 eps figures and a tabl