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The Time Evolution of Quantum Universe in the Quantum Potential Picture

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

We use the quantum potential approach to analyse the quantum cosmological model of the universe. The quantum potential arises from exact solutions of the full Wheeler-De Witt equation.

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The quantum potential approach makes it possible to construct a complementary picture of quantum mechanical evolution which reminds classical equation of motion. The only difference as compared to equations of motion for the underlying classical system is the presence of an additional potential term being a functional of the real part of the wavefunction. In the present paper this approach is applied to the quantum theory of gravity based on Wheeler -- De Witt equation. We describe the derivation of the `quantum Einstein equation' and discuss the new features of their solutions.
In this paper we discuss the quantum potential approach of Bohm in the context of a quantum cosmological model. This approach makes it possible to convert the wavefunction of the universe into a set of equations describing the time evolution of the universe. Following Ashtekar et al we make use of a quantum canonical transformation to cast a class of a quantum cosmological models into a simple form in which they can be solved explicitly, and then we use the solutions to recover the time evolution.
The quantum potential approach makes it possible to construct a complementary picture of quantum mechanical evolution which reminds classical equation of motion. The only difference as compared to equations of motion for the underlying classical system is the presence of an additional potential term being a functional of the real part of the wavefunction. In the present paper this approach is applied to the quantum theory of gravity based on Wheeler – De Witt equation. We describe the derivation of the ‘quantum Einstein equation ’ and discuss the new features of their solutions. It gives me great pleasure to contribute this article to the volume in honor of Professor Jerzy Lukierski. I clearly remember when, still being a student, I have met him for the first time during one of the winter Karpacz schools in late 1970s. Since then he was always close to me, first as an advisor and referee of my PhD thesis, and then as a close collaborator in many research projects and a very good friend. I cannot possibly fully pay my debt to him; let this article be at least an expression of acknowledgement of what I owe him. 2.