Moncy V. John

MODIFIED DE BROGLIE-BOHM APPROACH TO QUANTUM MECHANICS

A modified de Broglie-Bohm (dBB) approach to quantum mechanics is presented. In this new deterministic theory, which uses complex methods in an intermediate step, the problem of zero velocity for bound states encountered in the dBB formulation does not appear. Also, this approach is equivalent to standard quantum mechanics when averages of observables like position, momentum and energy are taken.

Cosmographic Evaluation of the Deceleration Parameter Using Type Ia Supernova Data

The apparent magnitude-redshift data of Type Ia supernovae (SNe Ia) call for modifications in the standard model energy densities. Under the circumstance that this modification cannot be limited to the addition of a mere cosmological constant, a serious situation has emerged in cosmology in which the energy densities in the universe have become largely speculative. In this situation, an equation of state of the form p = wρ itself is not well motivated. In this paper, we argue that the reasonable remaining option is to make a model-independent analysis of SNe data without reference to the energy densities. In this basically kinematic approach, we limit ourselves to the observationally justifiable assumptions of homogeneity and isotropy, i.e., to the assumption that the universe has a Robertson-Walker metric. This cosmographic approach is historically the original one in cosmology. We perform the analysis by expanding the scale factor into a fifth-order polynomial, an assumption that can be further generalized to any order. The present expansion rates h, q0, r0, etc., are evaluated by computing the marginal likelihoods for these parameters. These values are relevant since any cosmological solution would ultimately need to explain them.

Probability and complex quantum trajectories

Abstract It is shown that in the complex trajectory representation of quantum mechanics, the Born’s Ψ★Ψ probability density can be obtained from the imaginary part of the velocity field of particles on the real axis. Extending this probability axiom to the complex plane, we first attempt to find a probability density by solving an appropriate conservation equation. The characteristic curves of this conservation equation are found to be the same as the complex paths of particles in the new representation. The boundary condition in this case is that the extended probability density should agree with the quantum probability rule along the real line. For the simple, time-independent, one-dimensional problems worked out here, we find that a conserved probability density can be derived from the velocity field of particles, except in regions where the trajectories were previously suspected to be nonviable. An alternative method to find this probability density in terms of a trajectory integral, which is easier to implement on a computer and useful for single particle solutions, is also presented. Most importantly, we show, by using the complex extension of Schrodinger equation, that the desired conservation equation can be derived from this definition of probability density.

Generalized Chen-Wu type cosmological model

Recent measurements require modifications in conventional cosmology by way of introducing components other than ordinary matter into the total energy density in the universe. On the basis of some dimensional considerations in line with quantum cosmology, Chen and Wu [W. Chen and Y. Wu, Phys. Rev. D 41, 695 (1990)] have argued that an additional component, which corresponds to an effective cosmological constant

Comparison of cosmological models using Bayesian theory

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Cosmography, decelerating past, and cosmological models : Learning the Bayesian way

must vary as a^{-2} in the classical era. Their decaying-

Probability and complex quantum trajectories: Finding the missing links

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Coherent States and Modified de Broglie-Bohm Complex Quantum Trajectories

model assumes inflation and yields a value for q_{0}, which is not compatible with observations. We generalize this model by arguing that the Chen-Wu ansatz is applicable to the total energy density of the universe and not to

Exact classical correspondence in quantum cosmology

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Bayesian model-independent evaluation of expansion rates of the universe

alone. The resulting model, which has a coasting evolution (i.e.,