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    • 10: Quantum Physics
      https://phys.libretexts.org/Learning_Objects/A_Physics_Formulary/Physics/10%3A_Quantum_Physics
      Quantum mechanics, atomic physics, Schrödinger and Dirac equations
    • 2.1: Small changes to the Hamiltonian
      https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Physics_(Ackland)/02%3A_Review_-_Time-Independent_Non-degenerate_Perturbation_Theory/2.01%3A_Small_changes_to_the_Hamiltonian
      WLOG, consider a state \(i = 0\): the effect of the perturbation will be to modify the state and its corresponding energy slightly; The eigenstate \(|n_0 \rangle\) will become \(|\phi_0 \rangle\) and ...WLOG, consider a state \(i = 0\): the effect of the perturbation will be to modify the state and its corresponding energy slightly; The eigenstate \(|n_0 \rangle\) will become \(|\phi_0 \rangle\) and \(E_0\) will shift to \(E_0 + \Delta E_0\), where
    • 1.10: Quantum Physics
      https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Introductory_Physics_II_(1112)/zz%3A_Back_Matter/10%3A_13.1%3A_Appendix_J-_Physics_Formulas_(Wevers)/1.10%3A_Quantum_Physics
      Quantum mechanics, atomic physics, Schrödinger and Dirac equations
    • 8.2: Perturbation Theory
      https://phys.libretexts.org/Bookshelves/Thermodynamics_and_Statistical_Mechanics/Statistical_Mechanics_(Styer)/08%3A_Interacting_Classical_Fluids/8.02%3A_Perturbation_Theory
      \( \begin{array}{rlrl}{z=\rho+\mathcal{O}\left(z^{2}\right)} & {} & {z^{2}=\left(\rho+\mathcal{O}\left(z^{2}\right)\right)\left(\rho+\mathcal{O}\left(z^{2}\right)\right)} & {z^{3}} & {=\left(\rho^{2}+...\( \begin{array}{rlrl}{z=\rho+\mathcal{O}\left(z^{2}\right)} & {} & {z^{2}=\left(\rho+\mathcal{O}\left(z^{2}\right)\right)\left(\rho+\mathcal{O}\left(z^{2}\right)\right)} & {z^{3}} & {=\left(\rho^{2}+\mathcal{O}\left(z^{3}\right)\right)\left(\rho+\mathcal{O}\left(z^{2}\right)\right)} \\ {} & {=\rho^{2}+2 \rho \mathcal{O}\left(z^{2}\right)+\mathcal{O}\left(z^{4}\right)} & {} & {=\rho^{3}+\mathcal{O}\left(z^{4}\right)} \\ {} & {=\rho^{2}+\mathcal{O}\left(z^{3}\right)} & {} & {=\rho^{3}+\mathcal{O…

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