Boundary Conditions in Quantum Mechanics

1984 ◽  
Vol 52 (8) ◽  
pp. 573-576 ◽  
Author(s):  
Walter C. Henneberger
Keyword(s):  
Quantum Mechanics ◽  
Boundary Conditions

Transparent boundary conditions for discretized non-Hermitian eigenvalue problems

2021 ◽  
pp. 2150138
Author(s):  
Jonathan Heinz ◽  
Miroslav Kolesik
Keyword(s):  
Quantum Mechanics ◽  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Eigenvalue Problems ◽  
Complex Scaling ◽  
Transparent Boundary Conditions ◽  
Drastic Reduction ◽  
Optical Cavities ◽  
Energy Dependent ◽  
Lossy Waveguides

A method is presented for transparent, energy-dependent boundary conditions for open, non-Hermitian systems, and is illustrated on an example of Stark resonances in a single-particle quantum system. The approach provides an alternative to external complex scaling, and is applicable when asymptotic solutions can be characterized at large distances from the origin. Its main benefit consists in a drastic reduction of the dimesnionality of the underlying eigenvalue problem. Besides application to quantum mechanics, the method can be used in other contexts such as in systems involving unstable optical cavities and lossy waveguides.

scholarly journals Absorbing boundary conditions for relativistic quantum mechanics equations

2014 ◽  
Vol 277 ◽  
pp. 268-304 ◽  
Author(s):  
X. Antoine ◽  
E. Lorin ◽  
J. Sater ◽  
F. Fillion-Gourdeau ◽  
A.D. Bandrauk
Keyword(s):  
Quantum Mechanics ◽  
Boundary Conditions ◽  
Relativistic Quantum ◽  
Absorbing Boundary Conditions ◽  
Relativistic Quantum Mechanics ◽  
Absorbing Boundary

scholarly journals Irreversibility in quantum mechanics

2004 ◽  
Vol 2004 (1) ◽  
pp. 75-83 ◽  
Author(s):  
R. C. Bishop ◽  
A. Bohm ◽  
M. Gadella
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Boundary Conditions ◽  
Liouville Equation ◽  
Quantum Systems ◽  
Arrow Of Time ◽  
Time Asymmetry ◽  
Classical Physics ◽  
Von Neumann ◽  
Signal Features

Time asymmetry and irreversibility are signal features of our world. They are the reason of our aging and the basis for our belief that effects are preceded by causes. These features have many manifestations called arrows of time. In classical physics, some of these arrows are described by the increase of entropy or probability, and others by time-asymmetric boundary conditions of time-symmetric equations (e.g., Maxwell or Einstein). However, there is some controversy over whether probability or boundary conditions are more fundamental. For quantum systems, entropy increase is usually associated with the effects of an environment or measurement apparatus on a quantum system and is described by the von Neumann-Liouville equation. But since the traditional (von Neumann) axioms of quantum mechanics do not allow time-asymmetric boundary conditions for the dynamical differential equations (Schrödinger or Heisenberg), there is no quantum analogue of the radiation arrow of time. In this paper, we review consequences of a modification of a fundamental axiom of quantum mechanics. The new quantum theory is time asymmetric and accommodates an irreversible time evolution of isolated quantum systems.

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