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PLANE WAVE SOLUTIONS OF A QUANTUM FRACTIONAL SCHRöDINGER EQUATION AND UNCERTAINTY PRINCIPLE


Author : Muhammad I. Bhatti
[ Volume No.:VI, Issue No.II-Mar 2017] [Page No : 707-709] [2017]

Plane wave solutions of the fully fractional Schrödinger equation were proposed and represented in terms of exponential function. The plane wave solutions satisfied the fractional time-dependent Schrödinger equation. The Uncertainty Principle was obtained from the solution in the one-dimensional case using as a fractional order parameter of the space and time derivatives. For the integral value of the fractional parameter , the standard solution of the Schrödinger Equation was recovered. Some physical quantities such as the Mean Square Distance and expectation of the fractional momentum were evaluated. For the integral value of =1 the expressions of these physical quantities returned to standard quantum mechanical formulae.

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