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Foundational Physics Research Methods
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Module 5
Perturbation Theory and Variational Methods
1
Identifying Small Parameters for Perturbation Theory
Identify and classify small parameters in a physical problem suitable for a perturbative treatment.
2
Regular vs. Singular Perturbations
Distinguish between regular and singular perturbation problems.
3
Perturbative Expansion: Order and Convergence
Perform a perturbative expansion to a given order and assess its convergence.
4
Diagnosing Perturbative Expansion Breakdown
Diagnose the breakdown of a perturbative expansion via secular terms, divergences, or level crossings.
5
Variational Method for Ground States
Apply variational principles to obtain approximate ground state energies and wavefunctions.
6
Approximation Validity: Physical Arguments
Assess the domain of validity of an approximation using physical arguments.
Previous module
Constructing and Validating Toy Models
Next module
Asymptotic and Semiclassical Methods