Optical potentials in time dependent quantum systems: evaluation ofQ space probabilities

1990 ◽  
Vol 15 (2) ◽  
pp. 141-144 ◽  
Author(s):  
H. J. L�dde ◽  
A. Henne ◽  
R. M. Dreizler
Keyword(s):  
Quantum Systems ◽  
Time Dependent ◽  
Optical Potentials

scholarly journals A Realization of a Quasi-Random Walk for Atoms in Time-Dependent Optical Potentials

Atoms ◽  
2015 ◽  
Vol 3 (3) ◽  
pp. 433-449 ◽  
Author(s):  
Torsten Hinkel ◽  
Helmut Ritsch ◽  
Claudiu Genes
Keyword(s):  
Random Walk ◽  
Time Dependent ◽  
Optical Potentials

scholarly journals Time-Dependent Pseudo-Hermitian Hamiltonians and a Hidden Geometric Aspect of Quantum Mechanics

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 471 ◽  
Author(s):  
Ali Mostafazadeh
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Hermitian Operator ◽  
Quantum Systems ◽  
Time Dependent ◽  
Inner Product ◽  
Geometric Framework ◽  
Heisenberg Picture ◽  
Metric Operator ◽  
Recent Developments

A non-Hermitian operator H defined in a Hilbert space with inner product ⟨ · | · ⟩ may serve as the Hamiltonian for a unitary quantum system if it is η -pseudo-Hermitian for a metric operator (positive-definite automorphism) η . The latter defines the inner product ⟨ · | η · ⟩ of the physical Hilbert space H η of the system. For situations where some of the eigenstates of H depend on time, η becomes time-dependent. Therefore, the system has a non-stationary Hilbert space. Such quantum systems, which are also encountered in the study of quantum mechanics in cosmological backgrounds, suffer from a conflict between the unitarity of time evolution and the unobservability of the Hamiltonian. Their proper treatment requires a geometric framework which clarifies the notion of the energy observable and leads to a geometric extension of quantum mechanics (GEQM). We provide a general introduction to the subject, review some of the recent developments, offer a straightforward description of the Heisenberg-picture formulation of the dynamics for quantum systems having a time-dependent Hilbert space, and outline the Heisenberg-picture formulation of dynamics in GEQM.

Sign in / Sign up

Export Citation Format

Share Document