Trajectories and traversal times in quantum tunneling
The classical concepts of trajectories and traversal times applied to quantum tunneling are discussed. By using the Wentzel-Kramers-Brillouin approximation, it is found that in a forbidden region of a multidimensional space the wave function can be described by two sets of trajectories, or equivalently by two sets of wave fronts. The trajectories belonging to different sets are mutually orthogonal. An extended Huygens construction is proposed to determine these wave fronts and trajectories. In contrast to the classical results in the allowed region, these trajectories couple to each other. However, if the incident wave is normal to the turning surface, the trajectories are found to be independent and can be determined by Newton's equations of motion with inverted potential and energy. The multidimensional tunneling theory is then applied to the scanning tunneling microscope to calculate the current density distribution and to derive the expressions for the lateral resolution and the surface corrugation amplitude. The traversal time in quantum tunneling, i.e. tunneling time, is found to depend on model calculations and simulations. Computer simulation of a wave packet tunneling through a square barrier is performed. Several approaches, including the phase method, Larmor clock, and time-dependent barrier model, are investigated. For a square barrier, two characteristic times are found: One is equal to the barrier width divided by the magnitude of the imaginary velocity; the other is equal to the decay length divided by the incident velocity. It is believed that the tunneling time can only be defined operationally.
- Research Organization:
- Pennsylvania State Univ., Middletown, PA (United States)
- OSTI ID:
- 5597511
- Resource Relation:
- Other Information: Thesis (Ph.D.)
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
TUNNEL EFFECT
MATHEMATICAL MODELS
CLASSICAL MECHANICS
COMPUTERIZED SIMULATION
CURRENT DENSITY
EQUATIONS OF MOTION
HUYGENS PRINCIPLE
QUANTUM MECHANICS
SCANNING ELECTRON MICROSCOPY
TRAJECTORIES
WAVE FUNCTIONS
WAVE PACKETS
WKB APPROXIMATION
DIFFERENTIAL EQUATIONS
ELECTRON MICROSCOPY
EQUATIONS
FUNCTIONS
MECHANICS
MICROSCOPY
PARTIAL DIFFERENTIAL EQUATIONS
SIMULATION
661100* - Classical & Quantum Mechanics- (1992-)