The Gronwall form of the Schrodinger Equation for Helium

The 1937 paper of Gronwall which concerns an alternative form for the Schrodinger Equation of the 2-electron Helium problem is re-derived in a (hopefully) transparent (possibly pedestrian) manner.

Frobenius Solution for Legendre's Equation, Rodrigue's Formula and Normalization

The Frobenius solution to Legendre/s equation is developed in detail as is Rodrigue's formula, which is employed to normalize Legendre polynomials.

Continued Fraction Solutions to Hermite's, Legendre's and Laguerre's Differential Equation

The continued fraction method for solving differential equations is illustrated using three famous differential equations used in quantum chemistry.

Efficiency and Continuity in Public Finance: The Ottoman System of Taxation

Economic historians have recently emphasized the importance of integrating economic and historical approaches in studying institutions. The literature on the Ottoman system of taxation, however, has continued to adopt a primarily historical approach, using ad hoc categories of classification and explaining the system through its continuities with the historical precedent. This paper integrates economic and historical approaches to examine the structure, efficiency, and regional diversity of the tax system. The structure of the system made it possible for the Ottomans to economize on the transaction cost of measuring the tax base. Regional variations resulted from both efficient adaptations and institutional rigidities.

The Wave Equation for Stringed Instruments

An elementary derivation of the wave equation as applied to violin strings is given.

Guessing Solutions to the H-atom Schrodinger Equation

In teaching elementary quantum chemistry, the concept of eigenfunctionality is explored using the H-atom's Hamiltonian and various guessed functions. This is done in Cartesian coordinates, in Spherical Polar coordinates, and in Confocal Elliptical coordinates.