Quartic anharmonic oscillator with potential V(x)= x(2) + g(2)x4
was the first non-exactly-solvable problem tackled by the
newly-written Schroedinger equation in 1926. Since that time
thousands of articles have been published on the subject, mostly
about the domain of small g(2) (weak coupling regime), although
physics corresponds to g(2) ~ 1, and they were mostly about
energies.This book is focused on studying eigenfunctions as a
primary object for any g(2). Perturbation theory in g(2) for the
logarithm of the wavefunction is matched to the true semiclassical
expansion in powers of : it leads to locally-highly-accurate,
uniform approximation valid for any g(2) [0, ) 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.
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