The Inverse Problem of Quantum Tunneling

Mohsen Razavy

A Brief History of Quantum Tunneling Some Basic Questions Concerning Quantum Tunneling Simple Solvable Problems Time-Dependence of the Wave Function in One-Dimensional Tunneling Semiclassical Approximations Generalization of the Bohr - Sommerfeld Quantization Rule and its Application to Quantum Tunneling Gamow's Theory, Complex Eigenvalues, and the Wave Function of a Decaying State Tunneling in Symmetric and Asymmetric Local Potentials and Tunneling in Nonlocal and Quasi-Solvable Barriers Classical Descriptions of Tunneling Tunneling in Time-Dependent Barriers Decay Width and Scattering Theory The Method of Variable Reflection Amplitude Applied to Solve Multichannel Tunneling Problems Path Integral and Its Semi-Classical Approximation in Quantum Tunneling Heisenberg's Equations of Motion for Tunneling Wigner Distribution Function in Quantum Tunneling Decay Widths of Siegert States, Complex Scaling and Dilatation Transformation Multidimensional Quantum Tunneling Group and Signal Velocities Time-Delay, Reflection Time Operator and Minimum Tunneling Time More about Tunneling Time Tunneling of a System with Internal Degrees of Freedom Motion of a Particle in a Waveguide with Variable Cross Section and in a Space Bounded by a Dumbbell-Shaped Object Relativistic Formulation of Quantum Tunneling Inverse Problems of Quantum Tunneling Some Examples of Quantum Tunneling in Atomic and Molecular Physics Some Examples from Condensed Matter Physics Alpha Decay.

Neil Turok

G. Scharf, Walter Felipe Wreszinski, van +1 more

The tunnelling of a single quantum spin is studied in the limit of large spin quantum number S. The problem is mapped onto a particle problem on the positive half-line with a Hamiltonian which is invariant under inversion x to 1/x. Not only the ground-state energy but also all the other energy levels and corresponding level splittings (if any) are computed by using the conventional WKB methods for the particle problem and an excellent agreement with numerical data is found.

Zhenmin Wang

Based on the PFUSRC 45° triple coaxial bicone topology, cone-prism interlayer domain, and universal rigid axiom system, this paper reconstructs the ontological origin and dynamic framework of quantum tunneling. We strictly distinguish the 4D global space from the cone-prism interlayer quasi-void domain, and point out that quantum tunneling is not “penetration through a barrier” in ordinary space, but a directional propagation of wavefunctions along topological vertices inside the interlayer. This paper introduces the passive-autonomous behavior dichotomy into tunneling theory: passive influence is determined by interlayer geometry, vertex position, and boundary constraints; autonomous behavior originates from coupling-zero perturbations and ζ-element order control, manifesting as intrabarrier recollision, path selection, symmetry breaking, and cooperative tunneling of massive clusters. Recent authoritative experiments show that all anomalous tunneling phenomena can be uniformly explained as responses to conforming or inverse primordial bicone topology. When the structure is inverse to the optimal topology, obvious anomalies appear, which are defined as inverse primordial cone behaviors. The theory is self-consistent, falsifiable, and supported by reliable experimental evidence.

Mohsen Razavy