Limitations on the principle of stationary phase when it is applied to tunneling analysis

Abstract

Using a recently developed procedure - multiple wave packet decomposition - here we study the phase time formulation for tunneling/reflecting particles colliding with a potential barrier. To partially overcome the analytical difficulties which frequently arise when the stationary phase method is employed for deriving phase (tunneling) time expressions, we present a theoretical exercise involving a symmetrical collision between two identical wave packets and an one-dimensional rectangular potential barrier. Summing the amplitudes of the reflected and transmitted waves - using a method we call multiple peak decomposition - is shown to allow reconstruction of the scattered wave packets in a way which allows the stationary phase principle to be recovered.

arXiv comment17 pages, 2 figures

References in corpus (9)

• Unified time analysis of photon and (nonrelativistic) particle Tunnelling, and the Superluminal group-velocity problem
• Superluminal effects for quantum tunneling through two successive barriers
• Multibarrier tunneling
• More About Tunnelling Times, the Dwell Time, and the ``Hartman Effect"
• Universal Tunnelling Time in photonic Barriers
• Nonlocal reflection by photonic barriers
• Generalizations of Kijowski's time-of-arrival distribution for interaction potentials
• On Superluminal motions in photon and particle tunnelings
• Transient interference of transmission and incidence

Cited by in corpus (8)

• $SU(2)\otimes SU(2)$ bi-spinor structure entanglement induced by a step potential barrier scattering in two-dimensions
• Physical mechanism of superluminal traversal time: interference between multiple finite wave packets
• Stationary phase method and delay times for relativistic and non-relativistic tunneling particles
• Delay time computation for relativistic tunneling particles
• Relativistic tunneling and accelerated transmission
• Relation between phase and dwell times for quantum tunneling of a relativistically propagating particle
• The Exact Correspondence between Phase Times and Dwell Times in a Symmetrical Quantum Tunneling Configuration
• Delay Times for Symmetrized and Antisymmetrized Quantum Tunneling Configurations