• A K Rajagopal

Articles written in Proceedings – Section A

• A note on the generalisation of Hermite polynomials

• A general transform-gauss transform

• Double dispersion relations in quantum Statistical Mechanics—II

Double dispersion relations are given for the functions$$\gamma (12;3) = \frac{1}{i}\langle T\left( {\psi (1)\psi ^\dag (2)B (3)} \right)\rangle$$ common in many electron problems. Here ψ and ψT refer to electron destruction and creation operators, and B (3) is a boson or boson-like operator such as particle density, ion displacement, local spin, particle current density, or electron spin density. Consequences of Hermiticity properties and time reversal invariance as well as sum rules are established for the spectral density functions entering the double dispersion relations. A subtracted double dispersion relation is suggested for the corresponding vertex function. Details of the derivation and examples are given which were not included in an earlier brief report of this work.

• Three problems and their relevance?

Three problems are posed and their solutions (ranging from complete to partial) described. They are (i) the Hydrogen atom in an intense magnetic field; (ii) the thermodynamics of one-dimensional chain of continuous spins in an external magnetic field interactingvia Heisenberg interaction; and (iii) the pair correlation function in an interactingmaariys electron system. The relevance of these problems and their solution and various aspects of physics are stressed.

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