E-Locus - Institutional Repository of the University of Crete

Home Collections School/Department School of Sciences and Engineering Department of Mathematics and Applied Mathematics Post-graduate theses

Post-graduate theses

Current Record: 34 of 123

[Add to Basket]

Identifier

000446280

Title

Quantum hydrodynamics of gaussian wavepackets

Alternative Title

Κβαντική υδροδυναμική κυματοπακέτων gauss

Author

Διάκουλας, Μιχαήλ-Άγγελος

Thesis advisor

Μακράκης, Γεώργιος

Abstract

We study some basic aspects of the quantum hydrodynamics of Gaussian wave packets which evolve according to the linear Schrödinger equation. In particular we calculate Bohms’ quantum potential and the deviation between classical and quantum trajectories for the free particle, for a particle moving in linear potential and a particle trapped by a quadratic potential (harmonic oscillator). In the first two cases all calculations are performed analytically, but in the third case the deviation is computed numerically. The calculations imply some qualitative relation between the spectrum of the Schrödinger equation and the behaviour of the deviation, which must be further investigated for more complicated potentials like, for example, the quartic oscillator

Language

English

Subject

Bohm equations

Bohm trajectories

Caustics Burger's equation

Geometrical optics

Quantum potential

Schrodinger's equation

Wigner transformation

Γεωμετρική οπτική

Εξίσωση Burger's