Renormalization-group method for simple operator problems in quantum mechanics
TLDR
In this paper, the failure of conventional perturbation theory due to secularity is considered with renormalization-group tecniques in two operator problems, namely the quantum anharmonic oscillator and quantum parametric resonance.Abstract:
The failure of conventional perturbation theory due to secularity is considered with renormalization-group tecniques in two operator problems. Specifically, some results concerning the quantum anharmonic oscillator and quantum parametric resonance are obtained with a rather modest effort in comparison to other methods.read more
Citations
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Dynamical renormalization group approach to relaxation in quantum field theory
TL;DR: In this article, the real time evolution and relaxation of expectation values of quantum fields and of quantum states are computed as initial value problems by implementing the dynamical renormalization group (DRG).
Journal ArticleDOI
Classical and quantum oscillators of quartic anharmonicities: second-order solution
Anirban Pathak,Swapan Mandal +1 more
TL;DR: In this paper, an analytical solution up to the second order in the coupling constant λ is obtained for a classical quartic anharmonic oscillator by using Taylor series method.
Journal ArticleDOI
Functional renormalization group for quantized anharmonic oscillator
Sándor Nagy,Kornél Sailer +1 more
TL;DR: In this article, the authors applied functional renormalization group methods to the O(N) symmetric quantum anharmonic oscillator, considered as a 0 − 1 dimensional quantum field-theoric model, in the next-to-leading order of the gradient expansion of the irreducible effective action.
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Classical and quantum oscillators of sextic and octic anharmonicities
Anirban Pathak,Swapan Mandal +1 more
TL;DR: In this article, the Taylor series method was used to solve classical anharmonic oscillators up to the linear power of λ (anharmonic constant) by imposing fundamental commutation relations between position and momentum operators.
References
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TL;DR: Au sommaire as discussed by the authors developed the concepts of quantum mechanics with special examples and developed the perturbation method in quantum mechanics and the variational method for probability problems in quantum physics.
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Advanced mathematical methods for scientists and engineers
Carl M. Bender,Steven A. Orszag +1 more
TL;DR: A self-contained presentation of the methods of asymptotics and perturbation theory, methods useful for obtaining approximate analytical solutions to differential and difference equations is given in this paper.
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Singular-Perturbation Theory: An Introduction with Applications
TL;DR: In this paper, initial value problems of Oscillatory Type: 1. Precession of the planet Mercury 2. Krylov/Bogoliubov averaging 3. The multiscale technique 4. Linear overdamped initial-value problems of Overdamped Type: 5. Linear over-over-overdamped problems 6. Nonlinear overdamped problems 7. Boundary value problems 8. Linear scalar problems 9. Linear first-order systems 10.