A new general approximation scheme(NGAS) in quantum theory:application to the anharmonic- and double well oscillators

@article{Mahapatra2004ANG,
  title={A new general approximation scheme(NGAS) in quantum theory:application to the anharmonic- and double well oscillators},
  author={B. P. Mahapatra and Neil Andre Santi and N. B. Pradhan},
  journal={arXiv: Quantum Physics},
  year={2004}
}
A new scheme of approximation in quantum theory is proposed which is potentially applicable to arbtrary interacting systems. The method consists in in approximating the original Hamiltonian by one corresponding to a suitable exactly solvable system (with interaction) such that the "quantum average" of both are equal, thus forcing self-consistency.The method transcends the limitations of the variational method and the perturbation theory.The results are systematically improvable by the… 
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References

SHOWING 1-10 OF 12 REFERENCES

Stationary phase approximation of Feynman path integrals

SummaryFeynman's path integral formalism is used to consider the transition matrix elements of a harmonic oscillator as perturbed by an anharmonic potential $$\lambda \left( {m\omega ^2 /4l^2 }

Large order behavior of Perturbation theory

We examine the large-order behavior of perturbation theory for the anharmonic oscillator, a simple quantum-field-theory model. New analytical techniques are exhibited and used to derive formulas

Divergence of perturbation theory in quantum electrodynamics

An argument is presented which leads tentatively to the conclusion that all the power-series expansions currently in use in quantum electrodynamics are divergent after the renormalization of mass and

The renormalization group and critical phenomena

1. Introduction This paper has three parts. The first part is a simplified presentation of the basic ideas of the renormalization group and the ε expansion applied to critical phenomena , following

Nonrelativistic Quantum Mechanics

The Breakdown of Classical Mechanics Review of Classical Mechanics Elementary Systems One-Dimensional Problems More One-Dimensional Problems Mathematical Foundations Physical Interpretation

Introduction to solid state physics

Mathematical Introduction Acoustic Phonons Plasmons, Optical Phonons, and Polarization Waves Magnons Fermion Fields and the Hartree-Fock Approximation Many-body Techniques and the Electron Gas

Calculations with supersymmetric potentials.

  • BoyaKmiecikBohm
  • Materials Science, Mathematics
    Physical review. D, Particles and fields
  • 1987
Numerical solutions for two problems in one-dimensional supersymmetric quantum mechanics are presented, in which sense the double-well potential ${V}_{\mathrm{-}}}$(x) is a critical potential; increasing \ensuremath{\alpha}\ensureMath{\ge}3 the authors obtain a well-defined grouping of positive- and negative-parity levels, corresponding to an increasing barrier between the two wells.

The QCD vacuum, hadrons and superdense matter

Theoretical Introduction Phenomenology of the QCD Vacuum Euclidean Theory of Tunneling: From Quantum Mechanics to the Gauge Theories Instanton Ensemble in QCD Lattice QCD The QCD Correlation