Ladder operators for isospectral oscillators

We present, for the isospectral family of oscillator Hamiltonians, a systematic procedure for constructing raising and lowering operators satisfying any prescribed `distorted' Heisenberg algebra (including the $q$-generalization). This is done by means of an operator transformation implemented by a shift operator. The latter is obtained by solving an appropriate partial isometry condition in the Hilbert space. Formal representations of the non-local operators concerned are given in terms of pseudo-differential operators. Using the new annihilation operators, new classes of coherent states are constructed for isospectral oscillator Hamiltonians. The corresponding Fock-Bargmann representations are also considered, with specific reference to the order of the entire function family in each case.Comment: 13 page

Note on Coherent States and Adiabatic Connections, Curvatures

We give a possible generalization to the example in the paper of Zanardi and Rasetti (quant-ph/9904011). For this generalized one explicit forms of adiabatic connection, curvature and etc. are given.Comment: Latex file, 12 page

Efficient Investment in Children

Many would say that children are society's most precious resource. So, how should we invest in them? To gain insight into this question, a dynamic general equilibrium model is developed where children differ by ability. Parents invest time and money in their offspring, depending on their altruism. This allows their children to grow up as more productive adults. First, the efficient allocation is characterized. Next, this is compared with the outcome that arises when financial markets are incomplete. The situation where child-care markets are also lacking is then examined. Additionally, the consequences of impure altruism are analyzed.Investment in children; efficiency; imperfect financial markets; impure altruism; lack of child-care markets.

Vibrational spectroscopy analysis and molecular conformational stability of N-((3-methyl-1-(phenylsulfonyl)-1H-indol-2-yl)methyl) acetamide

The FTIR and FT Raman vibrational analysis and the fundamental modes of N-((3-methyl-1-(phenylsulfonyl)-1H-indol-2-yl)methyl) acetamide [N3MP2MA] have been carried out. On the basis of quantum chemical calculations in B3LYP/6-31G(d,p) and B3LYP/6-311++G(d,p) levels the geometric parameters, vibrational analysis have been obtained. The experimental vibrational data have been compared with the wavenumbers derived theoretically. The intramolecular contacts have been interpreted using natural bond orbital (NBO) and natural localized molecular orbital (NLMO) analysis. Important non-linear properties such as electric dipole moment and first hyperpolarizability of N3MP2MA have been computed using B3LYP quantum chemical calculations. Finally, the HOMO-LUMO energy gap and the Mulliken population analysis on atomic charges of the title compound has been calculated