The Ordering Ambiguity and Position Dependent Mass for Non- Relativistic Quantum Particle With Inter-Dimensional (D=1)

Abstract

By revisiting free particle v(x)=0 endowed with position dependent mass = 1 (1+ 2 ) 2 has d=1 (the inter-dimensional). Starting with the kinetic energy operator, we will try to solve the equation by simplification mathematical method to find energy spectrum, then get stander form for the energy whose dependent on the ordering ambiguity. Copy Right, IJAR, 2016,. All rights reserved. …………………………………………………………………………………………………….... Introduction:-Position dependent mass quantum particles in non-relativistic quantum theory have inspired researchers in the last few years [1-4]. They found new useful and interesting models help them in physical obstructions [5], semiconductors [6], quantum dot [7], quantum liquids [8], He-clusters [9] and metal clusters [10].Quantum mechanical particle endowed with PDM erupt in the system of quantum mechanics to solve more problems of a delicate nature like example: the m(x), kinetic energy and the momentum operator does not commute [11].In other side, they try to find a solution for the Schrödinger equation in d-dimensional by dependent a canonical transformation (PCT) method [12,13 ] under task change variables [14][15][16]. The eigenvalues and eigenfunctions are mapped for the exact solutions for Schrödinger equation [17][18][19].Recently, PCT for PDM-quantum particle introduced in d-dimensional [1]. The inter-one degeneracies associated with the isomorphism between angular momentum and dimensionality builds up the ladder of excited states for any given values e.g. nonzero and the radial quantum number . By choosing the parameters = = −1with the PCT method, it lead to get the Schrödinger equation with the effective potential( Poschl-Teller potential) [20].Here, we choose a free particle with = 0, the interdimensional = 1 and keeping on the von-Roos ordering in the general form + + = −1 , we will try to find a new formula for energy spectrum depend on position dependent mass parameters. Time -independent Schrödinger equation in one-dimensional by PCT method:-The stander form time-independent Schrödinger equation is given: − ℏ 2 2 2 2 + = (1)