https://gdpark.blog/tags/partition-function/Recent content in Partition Function on gdpark.blogHugoenFri, 23 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-05-chapter-4-practice-problems/Thu, 31 Dec 2015 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-05-chapter-4-practice-problems/Working through Chapter 4 problems on two-state systems, using the Boltzmann distribution and partition functions to nail expectation values and energy variance.https://gdpark.blog/posts/thermal-statistical-33-the-partition-function/Fri, 22 Apr 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-33-the-partition-function/A casual deep-dive into what the partition function Z actually means — from its German roots to why dividing by Z magically turns Boltzmann weights into real probabilities.https://gdpark.blog/posts/thermal-statistical-34-relationship-between-the-partition-function-and-state-functi/Sat, 23 Apr 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-34-relationship-between-the-partition-function-and-state-functi/We derive thermodynamic state functions like U, F, and S straight from the partition function Z — turns out one sneaky differential trick does all the heavy lifting!https://gdpark.blog/posts/thermal-statistical-35-partition-functions-for-a-two-level-system-and-the-harmonic/Sun, 24 Apr 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-35-partition-functions-for-a-two-level-system-and-the-harmonic/We check that the partition function formulas for U, C, and S actually make physical sense using a simple two-level system — and yep, at 0 K everything ends up in the ground state. Ohong~!https://gdpark.blog/posts/thermal-statistical-36-density-of-states-and-statistical-mechanics-of-the-ideal-gas/Mon, 25 Apr 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-36-density-of-states-and-statistical-mechanics-of-the-ideal-gas/We finally tackle the ideal gas and why we can actually compute Z for it — turns out independent subsystems make partition functions way more manageable lol.https://gdpark.blog/posts/thermal-statistical-38-quantum-concentration-and-thermal-de-broglie-wavelength/Tue, 26 Apr 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-38-quantum-concentration-and-thermal-de-broglie-wavelength/We grind through the ideal gas partition function integral step by step, then dig into what the result actually tells us about quantum concentration and the thermal de Broglie wavelength.https://gdpark.blog/posts/thermal-statistical-39-partition-function-for-indistinguishable-particles/Wed, 27 Apr 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-39-partition-function-for-indistinguishable-particles/Turns out Z_sys = (Z_1)^n only works for distinguishable particles — we break down why indistinguishable ones mess up the math using a simple two-level system.https://gdpark.blog/posts/thermal-statistical-40-the-grand-canonical-ensemble/Sun, 01 May 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-40-the-grand-canonical-ensemble/Chapter 22 extends our model to allow particle exchange alongside energy flow, diving into the grand canonical ensemble where both energy and particle number can fluctuate.https://gdpark.blog/posts/thermal-statistical-41-the-grand-partition-function/Sat, 18 Jun 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-41-the-grand-partition-function/We let particles flow freely and ask what happens to the partition function — turns out there’s a grand version Z_G derived straight from entropy!https://gdpark.blog/posts/thermal-statistical-42-grand-potential/Sun, 19 Jun 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-42-grand-potential/We define the grand potential Φ_G = -k_BT·ln(Z_G) by building on how F works in the canonical ensemble — because the partition function holds all the power, hehehe!https://gdpark.blog/posts/thermal-statistical-75-practice-problems-chapter-20/Fri, 23 Dec 2016 00:00:00 +0000https://gdpark.blog/posts/thermal-statistical-75-practice-problems-chapter-20/Work through Chapter 20 practice problems on high-temperature partition functions, thermodynamic quantities, and rotational energy levels for harmonic oscillators and diatomic molecules.