# Alternative analysis to perturbation theory in quantum mechanics

@article{MartinezCarranza2011AlternativeAT, title={Alternative analysis to perturbation theory in quantum mechanics}, author={Juan Martinez-Carranza and Francisco Soto-Eguibar and Hector M. Moya-Cessa}, journal={The European Physical Journal D}, year={2011}, volume={66}, pages={1-6} }

Abstract
We develop an alternative approach to the time independent perturbation theory in non-relativistic quantum mechanics. The method developed has the advantage to provide in one operation the correction to the energy and to the wave function; additionally we can analyze the time evolution of the system for any initial condition, which may be bothersome in the standard method. To verify our results, we apply our method to the harmonic oscillator perturbed by a quadratic potential. An… Expand

#### 10 Citations

Application of Perturbation Theory to a Master Equation

- Mathematics
- 2016

We develop a matrix perturbation method for the Lindblad master equation. The first- and second-order corrections are obtained and the method is generalized for higher orders. The perturbation method… Expand

Exact and approximated solutions for the harmonic and anharmonic repulsive oscillators: Matrix method

- Physics
- 2020

Abstract We study the repulsive harmonic oscillator and an extension of this system, with an additional linear anharmonicity term. The system is solved in exact and perturbative form, the latter by… Expand

Normalization corrections to perturbation theory based on a matrix method

- Physics, Mathematics
- 2018

We present the derivation of the normalization constant for the perturbation matrix method recently proposed. The method is tested on the problem of a binary waveguide array for which an exact and an… Expand

The su(1,1)-like intensity-dependent Rabi model: A perturbative analysis of weak and strong-coupling regimes

- Physics
- 2014

We present a perturbative analysis of a Rabi model where the coupling between the quantized single-mode electromagnetic field and the two-level atom depends on the field intensity. Upon modeling the… Expand

Explicit Description of the Zassenhaus Formula

- Physics, Mathematics
- 2017

We explicitly describe an expansion of $e^{A+B}$ as an infinite sum of the products of $B$ multiplied by the exponential function of $A$. This is the explicit description of the Zassenhaus formula.… Expand

Molecular dynamic investigation on the structures and thermal properties of carbon nanotube interfaces

- Materials Science
- 2015

Abstract The molecular dynamic (MD) simulations are performed to optimize the structures of the interface of carbon nanotubes and Cu nanowire. Thermal properties of their interfaces were studied on… Expand

Exploitation of Data Correlation and Performance Enhancement in Wireless Sensor Networks

- Computer Science
- 2015

Three algorithms are proposed in improving network energy efficiency, detecting data fault and reducing data redundancy, which have been studied to detect faulty data and aggregate redundant data by exploitation of spatial correlation. Expand

A novel R-PCA based multivariate fault-tolerant data aggregation algorithm in WSNs

- Computer Science
- 2016 IEEE International Conference on Communications (ICC)
- 2016

Recursion principal component analysis method is exploited to progressively update the transformation basis for extracting principal components and a novel R-PCA based algorithm is proposed to address data fault and data redundancy problems. Expand

Data Analytics and Performance Enhancement in Edge-Cloud Collaborative Internet of Things Systems

- Computer Science
- 2019

This thesis aims to address the related technical issues on IoT data processing and physical topology discovery of the subnets self-organized by IoT devices through the development of recursive principal component analysis (R-PCA) based data analysis framework. Expand

Recursive Principal Component Analysis-Based Data Outlier Detection and Sensor Data Aggregation in IoT Systems

- Computer Science
- IEEE Internet of Things Journal
- 2017

A cluster-based data analysis framework is proposed using recursive principal component analysis (R-PCA), which can aggregate the redundant data and detect the outliers in the meantime and efficiently aggregates the correlated sensor data with high recovery accuracy. Expand

#### References

SHOWING 1-10 OF 12 REFERENCES

Alternative quantum perturbation theory without divergences

- Physics
- 2000

A different integral form of the Schrodinger equation and some boundedness conditions of the wave functions are proved, which exhibit the origin of some divergences in quantum mechanics. The… Expand

A quick perturbative method for Schrödinger equations

- Mathematics
- 1997

Within the framework of perturbation theory we propose, firstly, an iterative method which may serve as a source of optimal unperturbed solutions in both one and more dimensions. It combines the… Expand

Coherent states for the time dependent harmonic oscillator: the step function

- Physics
- 2003

We study the time evolution for the quantum harmonic oscillator subjected to a sudden change of frequency. It is based on an approximate analytic solution to the time dependent Ermakov equation for a… Expand

Boundedness and convergence of perturbed corrections for helium-like ions in ground states

- Physics
- 2008

Applying the improved Rayleigh–Schrodinger perturbation theory based on an integral equation to helium-like ions in ground states and treating electron correlations as perturbations, we obtain the… Expand

Fifty years of eigenvalue perturbation theory

- Mathematics
- 1991

We highlight progres in the study of eigenvalue perturbation theory, especially problems connected to quantum mechanics. Six models are discussed in detail: isoelectronic atoms, autoionizing states,… Expand

The Radiation Theories of Tomonaga, Schwinger, and Feynman

- Physics
- 1949

A unified development of the subject of quantum electrodynamics is outlined, embodying the main features both of the Tomonaga-Schwinger and of the Feynman radiation theory. The theory is carried to a… Expand

Cavity quantum electrodynamics : the strange theory of light in a box

- Physics
- 2004

Preface. Acknowledgments. 1. Introduction. 2. Fiat Lux! 3. The Photon's Wavefunction. 4. A Box of Photons. 5. Let Matter Be! 6. Spontaneous Emission. 7. Macroscopic QED. 8. The Maser, the Laser, and… Expand

Diatomic Molecules According to the Wave Mechanics. II. Vibrational Levels

- Physics
- 1929

An exact solution is obtained for the Schroedinger equation representing the motions of the nuclei in a diatomic molecule, when the potential energy function is assumed to be of a form similar to… Expand

Electron-phonon coupling in transition metals and resonant scattering☆

- Physics
- 1973

Abstract An explicit formula is derived for the electron-phonon coupling of transition metals in terms of parameters that are used in first principle transition metal band structure calculations. Its… Expand