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QUANTUM ANHARMONIC OSCILLATOR IBD

ALEXANDER V TURBINER / JUAN CARLOS DEL VAL
WSPC
02 / 2023
9789811270451
Inglés

Sinopsis

Quartic anharmonic oscillator with potentialáV(x)=áx² +ág²xâü´ was the first non-exactly-solvable problem tackled by the newly-written Schrödinger equation in 1926. Since that time thousands of articles have been published on the subject, mostly about the domain of smallág² (weak coupling regime), although physics corresponds toág² ~ 1, and they were mostly about energies.This book is focused on studying eigenfunctions as a primary object for anyág². Perturbation theory inág² for the logarithm of the wavefunction is matched to the true semiclassical expansion in powers ofáâäÅ: it leads to locally-highly-accurate, uniform approximation valid for anyág²âêê[0,âêž) for eigenfunctions and even more accurate results for eigenvalues. This method of matching can be easily extended to the general anharmonic oscillator as well as to the radial oscillators. Quartic, sextic and cubic (for radial case) oscillators are considered in detail as well as quartic double-well potential.