I Solving Fermi-Dirac Integral: Step-by-Step Guide

arneet
Messages
8
Reaction score
0
i am completely lost. there is an integral in my textbook in fermi dirac statistics whose result is written directly and am not able to understand . it is
∫⌽(u) du /exp.((u-uf)/kt) + 1 from 0 to ∞
expanded by tayor's series to give

∫⌽(u) du (from 0 to uf) +∏²/6 (kT)² [⌽'(u)] |at u=uf + 7∏⁴/360 (kT)⁴ [⌽''(u)] |at u=uf +...

where uf is such that function of u is zero for u greater than uf.
please reply as soon as possible. thanks.
 
Physics news on Phys.org
It's very hard to read the formulae. Please use LaTeX.
 
hope this could help
 

Attachments

please reply. the answer on expansion by taylor series should be
 

Attachments

Thread 'Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and Education IBM) stated... Source: https://www.physicsforums.com/insights/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect/ by @RUTA
View full post »

Thread 'Quantum behaviour of an electron around a positively charged sphere'

If we release an electron around a positively charged sphere, the initial state of electron is a linear combination of Hydrogen-like states. According to quantum mechanics, evolution of time would not change this initial state because the potential is time independent. However, classically we expect the electron to collide with the sphere. So, it seems that the quantum and classics predict different behaviours!
View full post »

Thread 'Does a qubit break interference in the double slit experiment?'

According to recent podcast between Jacob Barandes and Sean Carroll, Barandes claims that putting a sensitive qubit near one of the slits of a double slit interference experiment is sufficient to break the interference pattern. Here are his words from the official transcript: Is that true? Caveats I see: The qubit is a quantum object, so if the particle was in a superposition of up and down, the qubit can be in a superposition too. Measuring the qubit in an orthogonal direction might...
View full post »

Similar threads

I General Concepts About Fermi-Dirac Distribution
Replies
8
Views
2K
I Solve Fermi-Dirac Integral: Get Help Now!
Replies
2
Views
2K
Quantum Mechanics- statistical physics fermi-dirac distribution.
Replies
4
Views
4K
Quantum QM Textbooks (Education + Research purposes)
Replies
3
Views
2K
Simple (Constant) Wavefunction -- Find Uncertainty In p^2
Replies
9
Views
2K
Understanding Band Gap Models in Statistical Mechanics: Qualifying Exam Practice
Replies
2
Views
3K
Time evolution in quantum field theories
2
Replies
79
Views
18K
BRS: The Weyl Vacuums. I. Definition, Geometrical Properties, Symmetries
Replies
11
Views
2K
Understanding E&M: A Review of Textbook Content and Critiques
Replies
1
Views
3K
Help in choosing 4 upper division physics classes.
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top