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It is shown how Cartan’s method of equivalence may be used to obtain the Cartan form for an r th-order particle Lagrangian on the line by solving the standard equivalence problem under contact transformations on the jet bundle J r+k for... more
It is shown how Cartan’s method of equivalence may be used to obtain the Cartan form for an r th-order particle Lagrangian on the line by solving the standard equivalence problem under contact transformations on the jet bundle J r+k for k≥r−1.
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We reply to the comment on our recent paper made by Drs Sinha and Roy. We agree that the backward Darboux transformation method used in our paper is equivalent to the approach based on CES potentials, but we stress that the emphasis and... more
We reply to the comment on our recent paper made by Drs Sinha and Roy. We agree that the backward Darboux transformation method used in our paper is equivalent to the approach based on CES potentials, but we stress that the emphasis and the results of our paper are different.
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ABSTRACT It has recently been proved [3] that the solution spaces of certain classes of differential equations whose local solutions are parametrized by three or four arbitrary constants can be endowed with conformal Lorentzian metrics in... more
ABSTRACT It has recently been proved [3] that the solution spaces of certain classes of differential equations whose local solutions are parametrized by three or four arbitrary constants can be endowed with conformal Lorentzian metrics in a natural way. We shall prove that these conformal structures are preserved when the differential equations are transformed by a contact transformation.
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We completely determine necessary and sufficient conditions for the normalizability of the wave functions giving the algebraic part of the spectrum of a quasi-exactly solvable Schrödinger operator on the line. Methods from classical... more
We completely determine necessary and sufficient conditions for the normalizability of the wave functions giving the algebraic part of the spectrum of a quasi-exactly solvable Schrödinger operator on the line. Methods from classical invariant theory are employed to provide a complete list of canonical forms for normalizable quasi-exactly solvable Hamiltonians and explicit normalizability conditions in general coordinate systems.