Stationary Perturbation Theory Applications

applications of stationary perturbation n.w

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Explore the applications of stationary perturbation theory in various subjects such as the unperturbed Hamiltonian, determining the scale of perturbation, and perturbing the hydrogen atom. Learn about estimating energy and wave functions, analyzing polynomial perturbations, and more.

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APPLICATIONS OF STATIONARY PERTURBATION THEORY NICOLE DREW GOPALAN STUDY GROUP, PSU OCTOBER 2, 2023

RECAP: UNPERTURBED HAMILTONIAN: KNOWN BASIS OF EIGENSTATES: PERTURBATION: DIMENSIONLESS PARAMETER:

RECAP: 2nd-order Estimate of nth (nondegenerate) Energy: 1st-order Estimate of nth (nondegenerate) Wave Function:

1D HARMONIC OSCILLATOR SUBJECT TO POLYNOMIAL PERTURBATIONS ?2 2?+1 2??2?2 ?0(?) = ?1? = ?1 ? ?2? = ?2 ?2 0= ? ? +1 ?3? = ?3 ?3 ?? 2 1 4 ?? ? 1 ?? ? ? ?? 2 ?2 ??? = 2? ?! ??

DETERMINING SCALE OF PERTURBATION ?2 2?+1 = 2 2? ??3 ? = ?1 ?1? = ?1 ? 2??2?2 ?2 ??2+1 ?0(?) = ?1 ?1 ??3 ?? ? ?1= = 2??2?2 ?1? = ?1 ?? ? = ?1 ? ? ?2 ??2+?? 2?? 2 ?2 = ? ?2(?) = ?2?2 = ?2 ??2 ?2 ?2 ?2 ?? ? ?2= = ??2 ???2 = ?2 ? ?2 ?? ?2? = ?2 ? = ? ?2 ??2+1 ?0(?) = ? 1 ?3?5 3 2 2?2 ?3? = ?3 ?3 ?3 = ?3 2 ?3 ?? ? ?3= = ?3 ?3?5 1/4 3 2 1 ? 1 2? ?! ??? ? 1 2 2 ??? = ?3 = ?3 ? ?3 ?3(?) = ?3 ??