Quantum anharmonic oscillator: The airy function approach

2014 ◽  
Vol 441 ◽  
pp. 17-20 ◽  
Author(s):  
F. Maiz ◽  
S. AlFaify
Keyword(s):  
Anharmonic Oscillator ◽  
Airy Function ◽  
Function Approach

Anharmonic oscillator analysis using modified Airy functions

1992 ◽  
Vol 70 (12) ◽  
pp. 1218-1221 ◽  
Author(s):  
I. C. Goyal ◽  
Sukhdev Roy ◽  
A. K. Ghatak ◽  
R. L. Gallawa
Keyword(s):  
Anharmonic Oscillator ◽  
Airy Function ◽  
Closed Form Expression ◽  
Airy Functions ◽  
Form Expression ◽  
Eighth Order ◽  
First Order ◽  
Numerical Effort ◽  
Modified Airy Functions ◽  
First Order Perturbation

We have applied the modified Airy function (MAF) method to the analysis of an anharmonic oscillator, characterized by the potential V(x) = k x2/2 + a x4, k > 0, a > 0. The MAF method gives an accurate closed-form expression for the wave function as well as very accurate eigenvalues with much less numerical effort than the five-term (eighth-order) WKBJ approximation. The application of the first-order perturbation correction to the MAF eigenvalues makes them even more accurate than those obtained by the five-term WKBJ approximation.

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