# Questions tagged [perturbation-theory]

Perturbation theory refers to methods for understanding physical systems by treating them as small modifications to exactly solvable systems.

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### Is the Rayleigh–Schrödinger perturbation theory ever useful for a many-body system?

The Rayleigh-Schrodinger perturbation theory is introduced in every textbook on quantum mechanics. It seems that it can yield accurate results for many single-particle systems. Actually, in most ...
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### Propagators in Frequency Space and Dyson's Expansion

I am reading the book Topics in Advanced Quantum Mechanics by Holstein. In the book (chapter 1.2) he shows that the time evolution operator $U(t)$ (for a Hamiltonian $H = H_0 + V$, with $V$ time ...
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### Does classical simple harmonic motion violate thermodynamics?

If SHM allows for motion to occur forever, we can consider it perpetual motion, does this imply that the second law of thermodynamics is violated? Or does the presence of an external force act on the ...
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### Adding an Impurity as a Perturbation to a Simulation

I am working on some plots corresponding to superconductors (of many kinds). If we insert a vortex, we can view this as an impurity and observe the Quasi-Particle-Interference (QPI). How I go about ...
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### Second order degenerate perturbation theory for a 4-level system

I am trying to find the second-order energy correction for a perturbation to a 4-level system $$H = H_0 + \lambda V.$$ I only care about corrections to the lowest energy, which is non-degenerate, ...
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### Second-Order Perturbation in electron gas

I was trying to figure out the solution to exercise 1.4 on Quantum theory of many particles systems by Fetter & Walecka and I read through this question and its answer. But a point made in both ...
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### Is there a counterexample to this pattern in QM perturbation theory?

Consider some $1d$ system $H_0$ with energy levels $E_n^{(0)}$ that has been perturbed by $\lambda V$, i.e. $H = H_0 + \lambda V$ for some $\lambda >0$. Consider the ratio of the first order ...
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### Doubt regarding Degenerate perturbation theory

McIntyre, quantum mechanics,pg360 Suppose states $\left|2^{(0)}\right\rangle$ and $\left|3^{(0)}\right\rangle$ are degenerate eigenstates of unperturbed Hamiltonian $H$. The first-order perturbation ...
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