Topics in Quantum Mechanics

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Such theories as quantum fields and strings have had a fruitful impact on certain developments in mathematics and have the sparked the interests of mathematicians towards a further understanding of some of the basic elements of these physical theories. This monograph navigates through the basic elements of quantum mechanics for a readership of mathematical researchers and graduate students whose background in physics might be rather modest. It should also be of interest to students and researchers in physics. Features include: topics such as Feynman path integrals, quantum statistical partition functions, high and low temperature asymptotics of quantum fields over a negatively curved space-time; a systematic application of the Nikiforov-Uvarov theory of generalised hypergeometric differential equations to solve the Schrodinger equation and to obtain the quantization of energies from a single elegant point of view; application of zeta functions, the Jacobi inversion formula, spherical harmonic analysis and the Selberg trade formula.