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New perturbation method with the matching of wave functions

Miloslav Znojil

We propose a new approach to the Rayleigh-Schrödinger perturbation expansions of bound states in quantum mechanics. We are inspired by the enormous flexibility of solvable interactions with several (N) discontinuities. Their standard matching solution is modified and transferred in perturbation regime. We employ the global renormalization freedom of the local wave functions and derive a compact N-dimensional matrix formula for corrections. In applications, our recipe is shown non-numerical for all polynomial perturbations of any piece-wise constant zero order potential.We propose a new approach to the Rayleigh-Schrödinger perturbation expansions of bound states in quantum mechanics. We are inspired by the enormous flexibility of solvable interactions with several (N) discontinuities. Their standard matching solution is modified and transferred in perturbation regime. We employ the global renormalization freedom of the local wave functions and derive a compact N-dimensional matrix formula for corrections. In applications, our recipe is shown non-numerical for all polynomial perturbations of any piece-wise constant zero order potential.

arXiv:quant-ph/9812027Dec 14, 19980 citations

Perturbation Theory in Quantum Mechanics

Francisco Marcelo Fernández

The standard textbook formulas for the perturbation corrections are somewhat cumbersome for a systematic calculation of sufficiently high order. In this book we show several alternative strategies that are easily programmable for numerical or algebraic calculation. We are mainly concerned with the derivation of exact perturbation corrections, and therefore concentrate on sufficiently simple nontrivial models having physical application. However, some of the algorithms discussed in this book are also suitable for numerical calculation.The standard textbook formulas for the perturbation corrections are somewhat cumbersome for a systematic calculation of sufficiently high order. In this book we show several alternative strategies that are easily programmable for numerical or algebraic calculation. We are mainly concerned with the derivation of exact perturbation corrections, and therefore concentrate on sufficiently simple nontrivial models having physical application. However, some of the algorithms discussed in this book are also suitable for numerical calculation.

CRC Press eBooksSep 19, 20002 citations

Perturbed Operators in Hilbert Space

Theodore W. Palmer

Perturbed operators in Hilbert space in justification of Rayleigh-Schroedinger perturbation theory in quantum chemistry

Sep 25, 19640 citations

New perturbation method with the matching of wave functions

Miloslav Znojil

We propose a new approach to the Rayleigh–Schrödinger perturbation expansions of bound states in quantum mechanics. We are inspired by the enormous flexibility of solvable interactions with several (N) discontinuities. Their standard matching solution is modified and transferred in perturbation regime. We employ the global renormalization freedom of the local wave functions and derive a compact N-dimensional matrix formula for corrections. In applications, our recipe is shown non-numerical for all polynomial perturbations of any piecewise constant zero-order potential. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 235–242, 2000We propose a new approach to the Rayleigh–Schrödinger perturbation expansions of bound states in quantum mechanics. We are inspired by the enormous flexibility of solvable interactions with several (N) discontinuities. Their standard matching solution is modified and transferred in perturbation regime. We employ the global renormalization freedom of the local wave functions and derive a compact N-dimensional matrix formula for corrections. In applications, our recipe is shown non-numerical for all polynomial perturbations of any piecewise constant zero-order potential. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 235–242, 2000

International Journal of Quantum ChemistryJan 1, 20004 citations

New perturbation method with the matching of wave functions

Miloslav Znojil

We propose a new approach to the Rayleigh–Schrödinger perturbation expansions of bound states in quantum mechanics. We are inspired by the enormous flexibility of solvable interactions with several (N) discontinuities. Their standard matching solution is modified and transferred in perturbation regime. We employ the global renormalization freedom of the local wave functions and derive a compact N-dimensional matrix formula for corrections. In applications, our recipe is shown non-numerical for all polynomial perturbations of any piecewise constant zero-order potential. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 235–242, 2000We propose a new approach to the Rayleigh–Schrödinger perturbation expansions of bound states in quantum mechanics. We are inspired by the enormous flexibility of solvable interactions with several (N) discontinuities. Their standard matching solution is modified and transferred in perturbation regime. We employ the global renormalization freedom of the local wave functions and derive a compact N-dimensional matrix formula for corrections. In applications, our recipe is shown non-numerical for all polynomial perturbations of any piecewise constant zero-order potential. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 235–242, 2000

International Journal of Quantum ChemistryJan 1, 20000 citations

A simple iterative method to write the terms of any order of perturbation theory in quantum mechanics

L. Bracci, Luigi E. Picasso

The European Physical Journal PlusOct 1, 20128 citations

Numerical Constructions of Perturbation Series in Quantum Mechanics

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Numerical Constructions of Perturbation Series in Quantum Mechanics

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