相关论文: Complex Energies and Beginnings of Time Suggest a …
Certain aspects of some unitary quantum systems are well-described by evolution via a non-Hermitian effective Hamiltonian, as in the Wigner-Weisskopf theory for spontaneous decay. Conversely, any non-Hermitian Hamiltonian evolution can be…
A possible solution of the problem of time in the Wheeler - DeWitt quantum geometrodynamics is that time appears in semiclassical limit. Following this line of thinking, one can come to the Schrodinger equation for matter fields in curved…
A relativistic resonance which was defined by a pole of the $S$-matrix, or by a relativistic Breit-Wigner line shape, is represented by a generalized state vector (ket) which can be obtained by analytic extension of the relativistic…
Deterministic dynamical models are discussed which can be described in quantum mechanical terms. In particular, a local quantum field theory is presented which is a supersymmetric classical model. -- The Hilbert space approach of Koopman…
The scattering theory of Lax and Phillips, designed primarily for hyperbolic systems, such as electromagnetic or acoustic waves, is described. This theory provides a realization of the theorem of Foias and Nagy; there is a subspace of the…
A quantum mechanical theory is proposed which abandons an external parameter ``time'' in favor of a self-adjoint operator on a Hilbert space whose elements represent measurement events rather than system states. The standard quantum…
We introduce a `proper time' formalism to study the instability of the vacuum in a uniform external electric field due to particle production. This formalism allows us to reduce a quantum field theoretical problem to a quantum-mechanical…
We begin with a description of spacetime by a 4-dimensional cubic lattice $\sscript$. It follows from this framework that the the speed of light is the only nonzero instantaneous speed for a particle. The dual space $\sscripthat$…
The exact solution of the Hamiltonian constraint in canonical gravity and the resultant reduction of Einstein's theory reveal the synergy between gravitation and the intrinsic cosmic clock of our expanding universe. Intrinsic Time…
We consider the process of diffusion scattering of a wave function given on the phase space. In this process the heat diffusion is considered only along momenta. We write down the modified Kramers equation describing this situation. In this…
We study the theory of scattering for a Schr"odinger equation in an external time dependent magnetic field in the Coulomb gauge, in space dimension 3. The magnetic vector potential is assumed to satisfy decay properties in time that are…
Physical laws for elementary particles can be described by the quantum dynamics equation given a Hamiltonian. The solution are probability amplitudes in Hilbert space that evolve over time. A probability density function over position and…
We exemplify the way the rigged Hilbert space deals with the Lippmann-Schwinger equation by way of the spherical shell potential. We explicitly construct the Lippmann-Schwinger bras and kets along with their energy representation, their…
The nature of time in quantum mechanics is closely related to the use of a complex, rather than say real, Hilbert space. This becomes particularly clear when considering quantum field theory in time dependent backgrounds, such as in…
The construction of exactly-solvable models has recently been advanced by considering integrable $T\bar{T}$ deformations and related Hamiltonian deformations in quantum mechanics. We introduce a broader class of non-Hermitian Hamiltonian…
A generalised equivalence principle is put forward according to which space-time symmetries and internal quantum symmetries are indistinguishable before symmetry breaking. Based on this principle, a higher-dimensional extension of Minkowski…
We consider an open quantum system which contains unstable states. The time evolution of the system can be described by an effective non-hermitian Hamiltonian H_{eff}, in accord with the Wigner--Weisskopf approximation, and an additional…
In order to resolve the measurement problem of Quantum Mechanics, non-unitary time evolution has been derived from the unitarity of standard quantum formalism. New wave functions of free and non-free quantum systems follow from Schroedinger…
We apply Brunetti and Fredenhagen's [Phys. Rev. A 66 (2002) 044101] concept of the time of occurrence of an event in quantum mechanics to the example of scattering off a spherical potential. Thereby, we re-derive the expression of…
The aim of the lecture is to briefly describe the mathematical background of scattering theory for two- and three-particle quantum systems. We discuss basic objects of the theory: wave and scattering operators and the corresponding…