scholarly journals An asymptotic functional-integral solution for the Schrödinger equation with polynomial potential

2009 ◽  
Vol 257 (4) ◽  
pp. 1030-1052 ◽  
Author(s):  
S. Albeverio ◽  
S. Mazzucchi
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Functional Integral ◽  
Integral Solution ◽  
Polynomial Potential

scholarly journals FUNCTIONAL-INTEGRAL SOLUTION FOR THE SCHRÖDINGER EQUATION WITH POLYNOMIAL POTENTIAL: A WHITE NOISE APPROACH

2011 ◽  
Vol 14 (04) ◽  
pp. 675-688 ◽  
Author(s):  
SONIA MAZZUCCHI
Keyword(s):  
Weak Solution ◽  
Schrödinger Equation ◽  
Integral Representation ◽  
White Noise ◽  
Schrodinger Equation ◽  
Functional Integral ◽  
Integral Solution ◽  
Polynomial Potential ◽  
White Noise Functional ◽  
Functional Integral Representation

A functional integral representation for the weak solution of the Schrödinger equation with polynomially growing potentials is proposed in terms of a white noise functional.

scholarly journals Group analysis and variational principle for nonlinear (3+1) schrodinger equation

2010 ◽  
Vol 7 (1) ◽  
pp. 115-122
Author(s):  
Eman Salem A. Alaidarous
Keyword(s):  
Variational Principle ◽  
Schrödinger Equation ◽  
Conservation Laws ◽  
Lie Groups ◽  
Schrodinger Equation ◽  
Group Analysis ◽  
Lie Symmetry ◽  
Functional Integral ◽  
Symmetry Groups ◽  
Conserved Currents

The generators of the admitted variational Lie symmetry groups are derived and conservation laws for the conserved currents are obtained via Noether's theorem. Moreover, the consistency of a functional integral are derived for the nonlinear Schrödinger equation. In addition to this analysis functional integral are studied using Lie groups.

Analytic Energies and Wave Functions of Two-Dimensional Schrödinger Equation: Two-Dimensional Fourth-Order Polynomial Potential

2008 ◽  
Vol 73 (10) ◽  
pp. 1327-1339 ◽  
Author(s):  
Vladimír Tichý ◽  
Lubomír Skála
Keyword(s):  
Schrödinger Equation ◽  
Fourth Order ◽  
Schrodinger Equation ◽  
Direct Method ◽  
Analytic Solutions ◽  
Wave Functions ◽  
Two Dimensional ◽  
Polynomial Potential ◽  
Order Polynomial ◽  
Fourth Order Polynomial

Direct method for searching analytic solutions of the two-dimensional Schrödinger equation with a two-dimensional fourth-order polynomial potential is presented. Analytic formulas for the energies and wave functions of the ground state and excited state are found. Obtained results can not be in general reduced to two one-dimensional cases.

Sign in / Sign up

Export Citation Format

Share Document