# 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…

## 5 Citations

### Square-Well Approximation for the Anharmonic and the Double-Well Oscillators

- Physics
- 2014

A novel general approximation scheme (NGAS) proposed earlier (ref.2-3) is applied to the problem of the quartic anharmonic (QAHO) and the double-well-oscillator (QDWO) in quantum theory by choosing…

### Perturbation Theory for Arbitrary Coupling Strength

- Physics
- 2016

We present a \emph{new} formulation of perturbation theory for quantum systems, designated here as: `mean field perturbation theory'(MFPT), which is free from power-series-expansion in any physical…

### The supersymmetric quantum mechanics theory and Darboux transformation for the Morse oscillator with an approximate rotational term

- PhysicsJournal of Mathematical Chemistry
- 2014

Anharmonic potentials with a rotational terms are widely used in quantum chemistry of diatomic systems, since they include the influence of centrifugal force on motions of atomic nuclei. For the…

### Exact solution of Schrödinger equation for Pseudoharmonic potential

- Physics
- 2007

Exact solution of Schrödinger equation for the pseudoharmonic potential is obtained for an arbitrary angular momentum. The energy eigenvalues and corresponding eigenfunctions are calculated by…

## References

SHOWING 1-10 OF 12 REFERENCES

### Stationary phase approximation of Feynman path integrals

- Physics
- 1967

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

- Physics
- 1971

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

- Physics
- 1952

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

- Physics
- 1983

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

- Physics
- 1985

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

- Physics
- 1953

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.

- Materials Science, MathematicsPhysical 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

- Physics
- 1988

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…