Ebook: Mathematical Results in Quantum Mechanics: International Conference in Blossin (Germany), May 17–21, 1993

The last decades have demonstrated that quantum mechanics is an inexhaustible source of inspiration for contemporary mathematical physics. Of course, it seems to be hardly surprising if one casts a glance toward the history of the subject; recall the pioneering works of von Neumann, Weyl, Kato and their followers which pushed forward some of the classical mathematical disciplines: functional analysis, differential equations, group theory, etc. On the other hand, the evident powerful feedback changed the face of the "naive" quantum physics. It created a contem­ porary quantum mechanics, the mathematical problems of which now constitute the backbone of mathematical physics. The mathematical and physical aspects of these problems cannot be separated, even if one may not share the opinion of Hilbert who rigorously denied differences between pure and applied mathemat­ ics, and the fruitful oscilllation between the two creates a powerful stimulus for development of mathematical physics. The International Conference on Mathematical Results in Quantum Mechan­ ics, held in Blossin (near Berlin), May 17-21, 1993, was the fifth in the series of meetings started in Dubna (in the former USSR) in 1987, which were dedicated to mathematical problems of quantum mechanics. A primary motivation of any meeting is certainly to facilitate an exchange of ideas, but there also other goals. The first meeting and those that followed (Dubna, 1988; Dubna, 1989; Liblice (in the Czech Republic), 1990) were aimed, in particular, at paving ways to East-West contacts.

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Content:
Front Matter....Pages i-x
Front Matter....Pages 1-1
Discrete spectrum of the periodic Schr?dinger operator for non-negative perturbations....Pages 3-7
The discrete spectrum in a gap of the continuous one for compact supported perturbations....Pages 9-12
Schr?dinger Operators with Strong Local Magnetic Perturbations: Existence of Eigenvalues in Gaps of the Essential Spectrum....Pages 13-18
Regularity of the nodal sets of solutions to Schr?dinger equations....Pages 19-25
Results in the spectral theory of Schr?dinger operators with wide potential barriers....Pages 27-32
Stark ladders and perturbation theory....Pages 33-36
Singular potentials: Algebraization....Pages 37-43
Asymptotic Behavior of the Resolvent of the Dirac Operator....Pages 45-54
Discrete spectrum of the perturbed Dirac operator....Pages 55-59
Front Matter....Pages 61-61
On the spectral properties of generalized Schr?dinger operators....Pages 63-72
A Fermi-type rule for contact embedded-eigenvalue perturbations....Pages 73-78
A Simple Model for Predissociation....Pages 79-87
Scattering on Several Solenoids....Pages 89-105
Hall conductance of Riemann surfaces....Pages 107-112
Front Matter....Pages 113-119
Framework and Results of Stochastic Spectral Analysis....Pages 121-121
Occupation time asymptotics with an application to the decay of eigenfunctions....Pages 123-132
Holomorphic semigroups and Schr?dinger equations....Pages 133-135
Some Problems on Submarkovian Semigroups....Pages 137-141
Smoothness Estimates and Uniqueness for the Dirichlet Operator....Pages 143-148
Front Matter....Pages 149-152
Trace Ideal Properties of Perturbed Dirichlet Semigroups....Pages 121-121
Front Matter....Pages 153-158
Quantum Dynamical Semigroups....Pages 159-159
Limits of Infinite Order, Dimensionality or Number of Components for Random Finite-Difference Operators....Pages 161-169
Atoms at Finite Density and Temperature and the Spectra of Reduced Density Matrices....Pages 171-189
Quantum Fluctuations in the Many-Body Problem....Pages 191-206
General Hamiltonians and Model Hamiltonians of the Theory of Superconductivity and Superfluidity in the Hilbert Space of Translation-Invariant Functions....Pages 207-212
Poisson Field Representations in the Statistical Mechanics of Continuous Systems....Pages 213-217
Exact ground states for quantum spin chains....Pages 219-226
The spectrum of the spin-boson model....Pages 227-232
A Survey oh Wigner-Poisson Problems....Pages 233-238
Front Matter....Pages 239-256
Classical d’Alembert field in an one-dimensional pulsating region....Pages 257-257
Irregular scattering in one-dimensional periodically driven systems.....Pages 259-262
Relatively Random Unitary Operators....Pages 263-275
Front Matter....Pages 277-280
A Trace Formula for Obstacles Problems and Applications....Pages 281-281
Propagation in Irregular Optic Fibres....Pages 283-292
Singular perturbations, regularization and extension theory....Pages 293-298
Adiabatic Reduction Theory. Semiclassical S-matrix for N-state one-dimensional systems.....Pages 299-305
The functional structure of the monodromy matrix for Harper’s equation....Pages 307-319
Eigenfunction expansion of right definite multiparameter problems....Pages 321-342
Singularly Perturbed Operators....Pages 343-346
Some Mathematical Problems of p-adic Quantum Theory....Pages 347-351
....Pages 353-356