Regular and Irregular Correspondences: Adiabatic Invariants in Classical and Quantum Mechanics

Semiclassical and Adiabatic Approximation in Quantum Mechanics

II. Semiclassical approximation 2 A. De…nition and criterion of validity 2 B. One-dimensional case: Intuitive consideration. 2 C. One-dimensional case: Formal derivation 2 D. Quantum penetration into classically forbidden region 3 E. Passing the turning point 3 F. The Bohr’s quantization rule 5 G. An excursion to classical mechanics 6 H. The under-barrier tunneling 7 I. Decay of a metastable st...

Mixing Quantum and Classical Mechanics

Using a group theoretical approach we derive an equation of motion for a mixed quantum-classical system. The quantum-classical bracket entering the equation preserves the Lie algebra structure of quantum and classical mechanics: The bracket is antisymmetric and satisfies the Jacobi identity, and, therefore, leads to a natural description of interaction between quantum and classical degrees of f...

Analysis of hydrofoil craft in regular and irregular waves

In this article, the most important specifications of hydrofoil floats, i.e. their seakeeping under regular and irregular waves under different encounter angles of wave, has been investigated. Numerical simulation has been done using STAR CCM+ software. Surge, heave, roll and pitch motions are kept free at the same time and their effects on each other are taken into account. USV01 model, whose ...

Added Resistance & Drift Force Analysis in Regular and Irregular Waves

The sea wave causes excess resistance which is out of scope of calm water resistance. The total wave force in horizontal plane is divided into “Added Resistance” and “Drift Force”. In this study, based on Gerritsma and Beuckelman[3] hypothesis a computer program has been developed for calculation of added resistance and drift force at various ship speeds and various head...

Supersymmetry in Quantum and Classical Mechanics