Legendre Polynomials and Angular Momentum

An introduction to Legendre polynomials as precursor to studying angular momentum in quantum chemistry,

Advance P. Chem. Problems (I) Populations, Partition Functions, Particle in Box, Harmonic Oscillators, Angular Momentum and Rigid Rotor

This is a set of P. Chem. problems posed at slightly higher than the normal text book level, for students who are continuing in the study of this subject.

Alternative Formulations for Angular Momentum Operators, Cartesian and Spherical Polar Forms

The conversion between representations of angular momentum in spherical polar and cartesian form is discussed.

Increasing Derivatives Market Activity in Emerging Markets and Exchange Rate Exposure

Understanding the effects of off-balance sheet transactions on interest and exchange rate exposures has become more important for emerging market countries that are experiencing remarkable growth in derivatives markets. Using firm level data, we report a significant fall in exposure over the past 10 years and relate this to higher derivatives market participation. Our methodology is composed of a three stage approach: First, we measure foreign exchange exposures using the Adler-Dumas (1984) model. Next, we follow an indirect approach to infer derivatives market participation at the firm level. Finally, we study the relationship between exchange rate exposure and derivatives market participation. Our results show that foreign exchange exposure is negatively related to derivatives market participation, and support the hedging explanation of the exchange rate exposure puzzle. This decline is especially salient in the financial sector, for bigger firms, and over longer time periods. Results are robust to using different exchange rates, a GARCH-SVAR approach to measure exchange rate exposure, and different return horizons.