3 research outputs found
Quantum Stephani Universe in vicinity of the symmetry center
We study a class of spherically symmetric Stephani cosmological models in the
presence of a self-interacting scalar field in both classical and quantum
domains. We discuss the construction of `canonical' wave packets resulting from
the solutions of a class of Wheeler-DeWitt equations in the Stephani Universe.
We suggest appropriate initial conditions which result in wave packets
containing some desirable properties, most importantly good classical and
quantum correspondence. We also study the situation from de-Broglie Bohm
interpretation of quantum mechanics to recover the notion of time and compare
the classical and Bohmian results. We exhibit that the usage of the canonical
prescription and appropriate choices of expansion coefficients result in the
suppression of the quantum potential and coincidence between classical and
Bohmian results. We show that, in some cases, contrary to
Friedmann-Robertson-Walker case, the bound state solutions also exist for all
positive values of the cosmological constant.Comment: 22 pages, 19 figures, to appear in JCA
An approach to construct wave packets with complete classical-quantum correspondence in non-relativistic quantum mechanics
We introduce a method to construct wave packets with complete classical and
quantum correspondence in one-dimensional non-relativistic quantum mechanics.
First, we consider two similar oscillators with equal total energy. In
classical domain, we can easily solve this model and obtain the trajectories in
the space of variables. This picture in the quantum level is equivalent with a
hyperbolic partial differential equation which gives us a freedom for choosing
the initial wave function and its initial slope. By taking advantage of this
freedom, we propose a method to choose an appropriate initial condition which
is independent from the form of the oscillators. We then construct the wave
packets for some cases and show that these wave packets closely follow the
whole classical trajectories and peak on them. Moreover, we use de-Broglie Bohm
interpretation of quantum mechanics to quantify this correspondence and show
that the resulting Bohmian trajectories are also in a complete agreement with
their classical counterparts.Comment: 15 pages, 13 figures, to appear in International Journal of
Theoretical Physic