APPLICATIONS OF REGULARIZED GREEN’S FUNCTION ON SCHRÖDINGER EQUATION OF 3D STRUCTURES WITH EXAMPLES

2017 ◽  
Vol 16 (1) ◽  
pp. 57-75
Author(s):  
M. Akram ◽  
S. Saadia ◽  
A. I. K. Butt
Keyword(s):  
Schrödinger Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Schrodinger Equation ◽  
3D Structures

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.

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