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mildra
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For a particle in a two-dimensional box. The particle is subject to perturbation V=Cxy. What are the eigenenergies and eigenfunctions of the unperturbed system and what is the first-order energy correction?
Perturbation theory is a mathematical approach used to solve problems in quantum mechanics that cannot be solved exactly. It involves breaking down a complex system into a simpler one, and then adding small corrections to the simpler system to approximate the behavior of the original system.
Perturbation theory involves expanding the wavefunction of a system in terms of a small parameter, such as the strength of an applied potential. The resulting series can be truncated at a certain order to approximate the exact solution. Higher orders in the series provide more accurate results.
Perturbation theory is only applicable to systems in which the perturbing potential is small compared to the unperturbed potential. Additionally, it assumes that the perturbations are small enough so that the system remains in the same quantum state throughout the calculation.
Perturbation theory is used in a variety of applications in quantum mechanics, such as calculating the energy levels of atoms and molecules, explaining the fine structure of spectral lines, and predicting the behavior of quantum systems in external fields.
No, perturbation theory is only applicable to certain types of problems in quantum mechanics. For example, it cannot be used to solve problems involving strong interactions or highly excited states. In these cases, other methods such as numerical techniques or approximation methods may be used.