A uniqueness theorem for higher order anharmonic oscillators

Quantum anharmonic oscillators: a new approach

Abstract. The determination of the eigenenergies of a quantum anharmonic oscillator consists merely in finding the zeros of a function of the energy, namely the Wronskian of two solutions of the Schrödinger equation which are regular respectively at the origin and at infinity. We show in this paper how to evaluate that Wronskian exactly, except for numerical rounding errors. The procedure is il...

Higher - Order Automated Theorem Proving for NaturalLanguage

This paper describes a tableau-based higher-order theorem prover Hot and an application to natural language semantics. In this application, Hot is used to prove equivalences using world knowledge during higher-order uniication (HOU). This extended form of HOU is used to compute the licensing conditions for corrections.

A quantum crystal with multidimensional anharmonic oscillators

The quantum anharmonic crystal is made of a large number of multi-dimensional anharmonic oscillators arranged in a periodic spatial lattice with a nearest neighbor coupling. If the coupling coefficient is sufficiently small, then there is a convergent expansion for the ground state of the crystal. The estimates on the convergence are independent of the size of the crystal. The proof uses the pa...

Higher-Order Automated Theorem Proving

The history of building automated theorem provers for higher-order logic is almost as old as the field of deduction systems itself. The first successful attempts to mechanize and implement higher-order logic were those of Huet [13] and Jensen and Pietrzykowski [17]. They combine the resolution principle for higher-order logic (first studied in [1]) with higher-order unification. The unification...

Higher-Order Automated Theorem Provers