Asymptotic perturbation theory

[qtm912]

Having just watched Prof Carl Bender's excellent 15 lecture course in mathematical physics on YouTube, the following question arose:
The approach was to work in one space dimension and to solve the Schrödinger equation for more general potentials than the harmonic oscillator using asymptotic theory. I was wondering how radically the maths changes when we work instead in three spatial dimensions.
Are the techniques developed, such as pade sequence, dominant balance and wkb somehow still applicable, but perhaps modified to solve PDEs,
Thanks

 

[DarMM]

Yes, but it's not a light topic and is still at research level without a nice introductory volume. Look at papers in Journal of Approximation Theory for example.