[Lesson 27] QED Prerequisites Laplace's Method, Stationary Phase

preview_player
Показать описание
This is the first of two lessons focusing on the critical asymptotic expression for the spherical Bessel functions. In this lesson we study the Laplace method for real integral representations of functions, and then the stationary phase method for a certain type of integral representation of a complex-valued function.

The software I usually use to produce the lectures is:

  1. XylyXylyX
Рекомендации по теме
[Lesson 27] QED 0:45:16

[Lesson 27] QED Prerequisites Laplace's Method, Stationary Phase

[Lesson 27.5 optional] 0:43:11

[Lesson 27.5 optional] QED Prerequisites Scattering 4.5 An application of Cauchy's Theorem

[Lesson 24] QED 0:53:30

[Lesson 24] QED Prerequisites Scattering I

[Lesson 20] QED 0:48:15

[Lesson 20] QED Prerequisites: Field Potentials from the Principle of Least Action

[Lesson 1] QED 1:17:54

[Lesson 1] QED Prerequisites Dirac Formalism Part I (redux)

[Lesson 25] QED 0:30:23

[Lesson 25] QED Prerequisites Scattering 2

IQ TEST 0:00:29

IQ TEST

Feb 10: Laplace's 0:19:49

Feb 10: Laplace's Method -- Additional Examples

Lecture 5: Stationary 1:32:56

Lecture 5: Stationary phase

Feb 8: Laplace's 0:50:32

Feb 8: Laplace's Method

[Lesson 18] Addendum 0:12:17

[Lesson 18] Addendum Lecture: The 'delta shorthand' notation

Towards Flow-based MCMC 1:16:22

Towards Flow-based MCMC for Lattice Gauge Theory with Fermions

Feb 12: Method 0:55:05

Feb 12: Method of Stationary Phase

Rouche's Theorem and 0:11:27

Rouche's Theorem and the Fundamental Theorem of Algebra

Lec 15: M/M/c 0:44:45

Lec 15: M/M/c Queues, Erlang Delay Formula

13. Derivation of 1:23:45

13. Derivation of optical Bloch equations

PH4209 : L17 0:27:36

PH4209 : L17 - Gauge DoF Redundancy

Prof. Dr. Pablo 0:28:41

Prof. Dr. Pablo Martin | Universidad de Antofagasta | Chile | Lecture | #Vebleo

Antti Kupiainen: Integrability 1:17:38

Antti Kupiainen: Integrability of Liouville Conformal Field Theory

Second Sem Electrodynamics 1:18:02

Second Sem Electrodynamics I: Thomas Precession (Dr. Madhav Prasad Ghimire, CDP, TU / 18 May 2020 )

SS_2022-06-24 2:11:35

SS_2022-06-24

Matrix (mathematics) | 1:18:31

Matrix (mathematics) | Wikipedia audio article

Комментарии
Автор

I always love dipping my toes into the world of asymptotics! For the stationary phase method, I believe the integral works identically to the usual Gaussian integral, just let a = -i*alpha. Thus Sqrt(Pi/a) = Sqrt(Pi/alpha)*Sqrt(1/-i) = Sqrt(Pi/alpha)*Exp(i*Pi/4). Great video, I look forward to the next in the series!

riakm
Автор

What happens if we have multiple maximum points of the same value (for Laplace’s Method)/stationary points (for the Method of Stationary Points)?

jy_decipherer_
Автор

Why not just make a quantum mechanics/topics in quantum mechanics playlist and then reference it once you start QED proper? Would probably get more hits on youtube just by changing the name. Anyways, great work as always.

aakashparikh