Abstract
Abstract The paper presents an first type boundary value problem for a Schrödinger equation. The aim of paper is to give the existence and uniqueness theorems of the boundary value problem using Galerkin’s method. Also, a priori estimate for its solution is given.
Highlights
The fundamental equation of quantum mechanics, Schrödinger eqution, is the basic non-relativistic wave equation which describes the behaviour of a single particle in a field of force
Its solution is called a wave function which give us information about the particle’s behavior in time and space and the square of the wave function states the probability of finding the location of an particle in a given area
We investigate the solutions of the boundary value problem (1.1)-(1.3) (BVP) under conditions (1.4)-(1.7)
Summary
The fundamental equation of quantum mechanics, Schrödinger eqution, is the basic non-relativistic wave equation which describes the behaviour of a single particle (on systems of particles) in a field of force. Schrödinger equation is a partial differential equation, that is, its solution is a function, not a number. The exact and numerical solutions of the various partial differential equations have been investigated by using the different methods in works [1,2,3,4,5], [7,8,9,10,11], [13,14], [16,17,18,19,20,21,22,23,24,25]. We investigate the solutions of the boundary value problem (1.1)-(1.3) (BVP) under conditions (1.4)-(1.7) For this purpose, we shall apply a well known Galerkin’s method to BVP. The solution of BVP is obtained as limits of approximate solutions calculated by this method [11]
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