We develop the theory of twisted L-cohomology and twisted spectral invariants for flat Hilbertian bundles over compact manifolds. They can be viewed as functions on H(M, R) and they generalize the standard notions. A new feature of the twisted L-cohomology theory is that in addition to satisfying the standard L Morse inequalities, they also satisfy certain asymptotic L Morse inequalities. These...

We develop the theory of twisted L-cohomology and twisted spectral invariants for flat Hilbertian bundles over compact manifolds. They can be viewed as functions on H(M, R) and they generalize the standard notions. A new feature of the twisted L-cohomology theory is that in addition to satisfying the standard L Morse inequalities, they also satisfy certain asymptotic L Morse inequalities. These...

Supersymmetry is a fundamental feature of quantum theory described by supersymmetric Hamiltonian comprised several mechanical Hamiltonians with different potentials that allows us to relate information about the states and spectra constituent Hamiltonians. In this paper we reconstruct Ioffe’s set for singular non-separable two-dimensional Morse potential using supersymmetry from non-degenerate ...

University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom San Diego Supercomputer Center, University of California, San Diego, USA Dipartimento di Informatica, Università di Torino, Corso Svizzera 185, I-10149 Torino, Italy Dipartimento di Sistemi e Informatica, Università di Firenze, Via di S.Marta, 3, I-50139 Firenze 185, Italy [email protected] • [email protected] • locate...

Morse theory could be very well be called critical point theory. The idea is that by understanding the critical points of a smooth function on your manifold, you can recover the topology of your space. This basic idea has blossomed into many Morse theories. For instance, Robin Forman developed a combinatorial adaptation called discrete morse theory. We also have Morse-Bott theory, where we cons...

The vibrational levels of diatomic molecules via Morse potentials are studied by means of the system confined in a spherical box of radius `. It is shown that there exists a critical radius `cr at which the spectrum of the usual unbounded system can be calculated to any desired accuracy. The results are compared with those of Morse’s classical solution which is based on the assumption that the ...