Numerical Solution of Time-Dependent Gravitational Schr\"{o}dinger Equation

POSTER

Abstract

In recent years, there are attempts to describe quantization of planetary distance based on time-independent gravitational Schr\"{o}dinger equation, including Rubcic {\&} Rubcic's method and also Nottale's Scale Relativity method. Nonetheless, there is no solution yet for time-dependent gravitational Schr\"{o}dinger equation (TDGSE). In the present paper, a numerical solution of time-dependent gravitational Schr\"{o}dinger equation is presented, apparently for the first time. This numerical solution leads to gravitational Bohr-radius, as expected. In the subsequent section, we also discuss plausible extension of this gravitational Schr\"{o}dinger equation to include the effect of phion condensate via Gross-Pitaevskii equation, as described recently by Moffat. Alternatively one can consider this condensate from the viewpoint of BogoliubovdeGennes theory, which can be approximated with coupled time-independent gravitational Schr\"{o}dinger equation. Further observation is of course recommended in order to refute or verify this proposition.

Authors

  • Milind Purohit

    Univ of South Carolina, Benedict College, Sc 29204, Univ. South Carolina, Benedict College, Univ South Carolina, GA Tech, Central Microscopy Research Facility, University of Iowa, Iowa City, Iowa 52242, USA, Department of Chemistry, University of Sri Jayewardenepura, Nugegoda, Sri Lanka, Department of Physics and Astronomy, Georgia State University, Atlanta, Georgia 30303, USA, Department of Chemistry, University of Alabama at Birmingham, Birmingham, AL 35294, Department of Physics, University of Alabama at Birmingham, Birmingham, AL 35294, College of William \& Mary, Harvard University, Benedict College, SC 29204, Massachusetts Institute of Technology, University of Applied Science, Bielefeld, Germany, Francis Marion University, Physics Dept., Emory University, Emory University, Formerly Emory University, currently UCLA, Physics Department, Georgia State University, Univ. of Georgia, Dept. of Chemistry, Universidad Nacional de Quilmes, Argentina, Pr, Dr, Derpartment of Physics, Florida A\&M University, Tallahassee, FL-32307, Department of Physics, Emory University, Georgia Institute of Technology, Naval Research Laboratory, University of Alabama, Tsinghua University, Lawrence Berkeley National Laboratory, Vanderbilt University, Jagellonian Univ., Univ. of Bonn, North Carolina A\&T State Univ., North Carolina Central Univ., Duke Univ. and TUNL, Georgia State University, Dept of Physics, Emory University, Cell Biology Department, Emory University, Physics Department, Emory University, University of South Carolina

  • Milind Purohit

    Univ of South Carolina, Benedict College, Sc 29204, Univ. South Carolina, Benedict College, Univ South Carolina, GA Tech, Central Microscopy Research Facility, University of Iowa, Iowa City, Iowa 52242, USA, Department of Chemistry, University of Sri Jayewardenepura, Nugegoda, Sri Lanka, Department of Physics and Astronomy, Georgia State University, Atlanta, Georgia 30303, USA, Department of Chemistry, University of Alabama at Birmingham, Birmingham, AL 35294, Department of Physics, University of Alabama at Birmingham, Birmingham, AL 35294, College of William \& Mary, Harvard University, Benedict College, SC 29204, Massachusetts Institute of Technology, University of Applied Science, Bielefeld, Germany, Francis Marion University, Physics Dept., Emory University, Emory University, Formerly Emory University, currently UCLA, Physics Department, Georgia State University, Univ. of Georgia, Dept. of Chemistry, Universidad Nacional de Quilmes, Argentina, Pr, Dr, Derpartment of Physics, Florida A\&M University, Tallahassee, FL-32307, Department of Physics, Emory University, Georgia Institute of Technology, Naval Research Laboratory, University of Alabama, Tsinghua University, Lawrence Berkeley National Laboratory, Vanderbilt University, Jagellonian Univ., Univ. of Bonn, North Carolina A\&T State Univ., North Carolina Central Univ., Duke Univ. and TUNL, Georgia State University, Dept of Physics, Emory University, Cell Biology Department, Emory University, Physics Department, Emory University, University of South Carolina

  • Florentin Smarandache

    University of New Mexico, Gallup Campus