https://gdpark.blog/tags/perturbation-theory/Recent content in Perturbation Theory on gdpark.blogHugoenTue, 29 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-27-time-independent-perturbation-theory/Wed, 23 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-27-time-independent-perturbation-theory/A casual intro to time-independent perturbation theory — what &lsquo;perturbed&rsquo; even means, why the real world is messy, and how approximation theory saves us.https://gdpark.blog/posts/quantum-mechanics-30-relativistic-correction-and-the-fine-structure-of-hydrogen/Fri, 25 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-30-relativistic-correction-and-the-fine-structure-of-hydrogen/Back to hydrogen with perturbation theory in hand — unpacking fine structure via relativistic correction, spin-orbit coupling, and Lamb shift, plus a prof quote that hit different.https://gdpark.blog/posts/quantum-mechanics-31-spin-orbit-coupling-ls-coupling-and-the-fine-structure-of-hy/Fri, 25 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-31-spin-orbit-coupling-ls-coupling-and-the-fine-structure-of-hy/We flip to the electron&rsquo;s reference frame and grind through Biot–Savart plus magnetic moments to build the spin-orbit correction to hydrogen&rsquo;s Hamiltonian.https://gdpark.blog/posts/quantum-mechanics-32-perturbation-theory-practice-problems/Fri, 25 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-32-perturbation-theory-practice-problems/Grinding through perturbation theory homework — a delta-function bump in an infinite square well, a tweaked harmonic oscillator, and why even-n states just don&rsquo;t care.https://gdpark.blog/posts/quantum-mechanics-33-van-der-waals-interaction-and-the-stark-effect/Fri, 25 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-33-van-der-waals-interaction-and-the-stark-effect/Turns out neutral atoms <em>do</em> attract each other — we Taylor-expand the Coulomb mess in Griffiths 6.31 to derive the Van der Waals interaction using perturbation theory.https://gdpark.blog/posts/quantum-mechanics-38-time-dependent-perturbation-theory/Sun, 27 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-38-time-dependent-perturbation-theory/We grind through the Schrödinger equation, pull the same bra-ket trick from Chapter 6, and land on coupled ODEs for C_a and C_b — with H&rsquo;_aa = H&rsquo;_bb = 0 for transitions.https://gdpark.blog/posts/quantum-mechanics-39-absorption-emission-and-stimulated-emission/Sun, 27 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-39-absorption-emission-and-stimulated-emission/We crank through sinusoidal perturbations on a two-level system and see how driving near resonance w₀ leads to absorption, emission, and stimulated emission.https://gdpark.blog/posts/quantum-mechanics-40-fermi-s-golden-rule-and-selection-rules/Mon, 28 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-40-fermi-s-golden-rule-and-selection-rules/We extend the monochromatic transition probability to polychromatic light, integrate over all frequencies, and arrive at Fermi&rsquo;s Golden Rule and the selection rules.https://gdpark.blog/posts/quantum-mechanics-42-chapter-9-practice-problems/Tue, 29 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/quantum-mechanics-42-chapter-9-practice-problems/Working through Chapter 9 practice problems on time-dependent perturbation theory, approximating the Dirac delta function with a rectangle and solving for the transition coefficients!