Time Dependent Green's Function for the s‐Dimensional Master Equation and Tight‐Binding Schrödinger Equation

1972 ◽  
Vol 56 (7) ◽  
pp. 3723-3724 ◽  
Author(s):  
William H. Butler
Keyword(s):  
Schrödinger Equation ◽  
Green’S Function ◽  
Master Equation ◽  
Green's Function ◽  
Schrodinger Equation ◽  
Tight Binding ◽  
Time Dependent

PATH INTEGRAL CALCULATION OF GREEN’S FUNCTION FOR SCHRÖDINGER EQUATION IN UNITARY GAUGE

1992 ◽  
Vol 07 (31) ◽  
pp. 7775-7786
Author(s):  
L. ROZANSKY
Keyword(s):  
Schrödinger Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Path Integral ◽  
Schrodinger Equation ◽  
Preexponential Factor ◽  
Unitary Gauge ◽  
Gauge Fixing

Green’s function of Schrödinger equation is represented as a time-reparametrization invariant path integral. Unitary gauge fixing enables us to get the WKB preexponential factor without calculating determinants of operators containing derivatives.

A simplified method for integrating over Feynman histories

1957 ◽  
Vol 53 (3) ◽  
pp. 651-653 ◽  
Author(s):  
S. G. Brush
Keyword(s):  
Quantum Mechanics ◽  
Fourier Series ◽  
Schrödinger Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Schrodinger Equation ◽  
Space Time ◽  
Simplified Method ◽  
Time Formulation

ABSTRACTIn Feynman's ‘space-time’ formulation of quantum mechanics the Green's function for the Schrödinger equation is defined by an integral over all histories of the system. By integrating over one-parameter sets of functions, one gets the same Green's function as by integrating over a Fourier series, in simple cases. The method may be useful for estimating the result in cases when the integration over all histories cannot be performed exactly.

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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