Canonical wave packets in quantum cosmology

2010

Ann. Phys.

We outline the applications of a new initial condition for the Wheeler-DeWitt equation in various quantum cosmology models. These models consist of minimally coupled scalar field in Friedmann-RobertsonWalker and Stephani spacetimes, varying speed of light theories and conformally coupled scalar field in Friedmann-Robertson-Walker spacetime. This initial condition results in wave packets with complete classical and quantum correspondence. This means that the wave packets closely follow the classical trajectories and strongly peak on them. We show that these models, similar to their classical counterparts, contain singularities even at the quantum level.

Section: The Modelmentioning

confidence: 71%

On the initial condition in quantum cosmology

2010

Ann. Phys.

“…It is worth to mention that this method has been used previously for some other similar cases [64,66,74,75].…”

Section: The Spectral Methodsmentioning

confidence: 99%

Chaplygin gas quantum universe in the presence of the cosmological constant

Jalalzadeh

2009

Gen Relativ Gravit

We present a Chaplygin gas Friedmann-Robertson-Walker quantum cosmological model in the presence of the cosmological constant. We apply the Schutz's variational formalism to recover the notion of time, and this gives rise to Wheeler-DeWitt equation for the scale factor. We study the early and late time universes and show that the presence of the Chaplygin gas leads to an effective positive cosmological constant for the late times. This suggests the possibility of changing the sign of the effective cosmological constant during the transition from the early times to the late times. For the case of an effective negative cosmological constant for both epoches, we solve the resulting Wheeler-DeWitt equation using the Spectral Method and find the eigenvalues and eigenfunctions for positive, zero, and negative constant spatial curvatures. Then, we use the eigenfunctions in order to construct wave packets for each case and obtain the time-dependent expectation value of the scale factors, which are found to oscillate between finite maximum and minimum values. Since the expectation value of the scale factors never tend to the singular point, we have an initial indication that this model may not have singularities at the quantum level.

“…However, since we are interested to construct wave packet with classical properties, we need to assume a specific relationship between these coefficients. The prescription is that the coefficients have the same functional form [25][26][27] i.e.…”

Section: The Modelmentioning

confidence: 99%

“…To fix the expansion coefficients, we will apply the prescription used in Refs. [25][26][27] for the case of hyperbolic PDEs which also appear in the context of quantum cosmology.…”

Section: Introductionmentioning

confidence: 99%

An Approach to Construct Wave Packets with Complete Classical-Quantum Correspondence in Non-relativistic Quantum Mechanics

2009

Int J Theor Phys

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 complete agreement with their classical counterparts.