Sources of quantum waves
arXiv:quant-ph/0007066 · doi:10.1088/0305-4470/34/20/303
Abstract
Due to the space and time dependence of the wave function in the time dependent Schroedinger equation, different boundary conditions are possible. The equation is usually solved as an ``initial value problem'', by fixing the value of the wave function in all space at a given instant. We compare this standard approach to "source boundary conditions'' that fix the wave at all times in a given region, in particular at a point in one dimension. In contrast to the well-known physical interpretation of the initial-value-problem approach, the interpretation of the source approach has remained unclear, since it introduces negative energy components, even for ``free motion'', and a time-dependent norm. This work provides physical meaning to the source method by finding the link with equivalent initial value problems.
12 pages, 7 inlined figures; typos corrected
References in corpus (5)
- Front Propagation in Evanescent Media
- Exact boundary conditions at finite distance for the time-dependent Schrodinger equation
- Analytical properties of scattering amplitudes in one-dimensional quantum theory
- Canonical pairs, Spatially Confined Motion and the Quantum Time of Arrival Problem
- Effect of classically forbidden momenta in one dimensional quantum scattering
Cited by in corpus (12)
- A measurement-based approach to quantum arrival times
- Time modulation of atom sources
- Matter wave pulses characteristics
- Enhanced observability of quantum post-exponential decay using distant detectors
- Transient response of a quantum wave to an instantaneous potential step switching
- Quantum-wave evolution in a step potential barrier
- Towards a time-reversal mirror for quantum systems
- Universal potential barrier penetration by initially confined wavepackets
- Testing the Equivalence Principle with Unstable Particles
- Atom laser dynamics in a tight-waveguide
- Comparison between two models of absorption of matter waves by a thin time-dependent barrier
- Dynamics of a quantum wave emitted by a decaying and evanescent point source