##  [Principle of Stationary Phase](/principle-stationary-phase) 

  ##  [Principle of Stationary Phase](https://mathlogic.quantumdictionary.io/principle-stationary-phase-0) 

  

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**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An asymptotic principle that the main contribution to a highly oscillatory integral ∫ a(x) e^{i k φ(x)} dx as the large parameter k → ∞ comes from neighborhoods of stationary points where φ'(x)=0 (and boundary points), with each nondegenerate stationary point contributing an explicit leading term determined by a(x), φ(x) and the Hessian of φ.