arXiv subjects
Publications and source records attributed to R. P. Venkataraman.
The necessary and sufficient conditions for differentiability of a function of several real variables stated and proved and its ramifications discussed.
For studying the thermodynamic properties of systems using statistical mechanics we propose an ensemble that lies in between the familiar canonical and microcanonical ensembles. From a comparative study of these ensembles we conclude that all these ensembles may not yield the same results even in the thermodynamic limit except at high temperatures. An investigation of the coupling between systems suggest that the state of thermodynamic equilibrium is a special case of statistical equilibrium. As a byproduct of this analysis we have obtained a general form for probability density function in an interval.
It is shown that Schroedinger equation is not consistent with information theory. From the modified form of information which ensures that the most probable density function it yields tallies with a general form of continuous Riemann integrable density function that has real or imaginary zeros or singularities at end points of $[a,b] εR$, a new variational formulation for quantum mechanics is proposed that yields a system of Euler-Lagrange equations that are non-linear. It is proved that the solutions of this system are unique, orthonormal and complete. One dimensional harmonic oscillator has been solved.