scholarly journals Hagedorn Wavepackets and Schrödinger Equation with Time-Dependent, Homogeneous Magnetic Field

2021 ◽  
pp. 110581
Author(s):  
Vasile Gradinaru ◽  
Oliver Rietmann
Keyword(s):  
Magnetic Field ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Homogeneous Magnetic Field ◽  
Time Dependent

scholarly journals Semiclassical quantization of circular billiard in homogeneous magnetic field: Berry-Tabor approach

2001 ◽  
Vol 26 (5) ◽  
pp. 269-280
Author(s):  
Gergely Palla ◽  
Gábor Vattay ◽  
József Cserti
Keyword(s):  
Magnetic Field ◽  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Density Of States ◽  
Schrodinger Equation ◽  
Homogeneous Magnetic Field ◽  
Leading Order ◽  
Trace Formulas ◽  
Semiclassical Methods ◽  
Semiclassical Quantization

Semiclassical methods are accurate in general in leading order ofħ, since they approximate quantum mechanics via canonical invariants. Often canonically noninvariant terms appear in the Schrödinger equation which are proportional toħ2, therefore a discrepancy between different semiclassical trace formulas in order ofħ2seems to be possible. We derive here the Berry-Tabor formula for a circular billiard in a homogeneous magnetic field. The formula derived for the semiclassical density of states surprisingly coincides with the results of Creagh-Littlejohn theory despite the presence of canonically noninvariant terms.

Introduction

2018 ◽  
Author(s):  
Niels Engholm Henriksen ◽  
Flemming Yssing Hansen
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Degrees Of Freedom ◽  
State Level ◽  
Boltzmann Distribution ◽  
Theoretical Description ◽  
Time Dependent ◽  
Nuclear Dynamics ◽  
Molecular Reaction ◽  
Oppenheimer Approximation

This introductory chapter considers first the relation between molecular reaction dynamics and the major branches of physical chemistry. The concept of elementary chemical reactions at the quantized state-to-state level is discussed. The theoretical description of these reactions based on the time-dependent Schrödinger equation and the Born–Oppenheimer approximation is introduced and the resulting time-dependent Schrödinger equation describing the nuclear dynamics is discussed. The chapter concludes with a brief discussion of matter at thermal equilibrium, focusing at the Boltzmann distribution. Thus, the Boltzmann distribution for vibrational, rotational, and translational degrees of freedom is discussed and illustrated.

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