Continuation of the recently increasingly popular numerical and
perturbative experiments studying purely imaginary anharmonicities.
The paper describes their extremely important extension to two and
three dimensions. In two dimensions the author emphasizes the
difference between even-even cases (where the spectra are general
complex and nothing interesting happens) and the other possibilities
where PT symmetric quantum mechanics applies (i.e., Hamiltonians may
be interpreted as pseudo-Hermitian and their energies may be either
real or arranged in complex conjugate doublets). It is emphasized
that in contrast to the one-dimensional case, P is not the standard
parity but rather a more general operator of reflection. The
structure of the sample spectra is very instructive in exhibiting the
unavoided crossings of levels, the confluence of pairs of opposite
quasi-parity followed by their complexification called spontaneous
symmetry breaking, etc. Detailed formulae are provided for the
linear-linear ``anharmonicity" (in fact, the mere rotated
harmonic-harmonic exactly solvable special case) and then for the
genuine linear-cubic and linear-linear-quadratic perturbatively and
variationally tractable anharmonicities.


CNO: 1952072 Nanayakkara, Asiri .
Real eigenspectra in non-Hermitian multidimensional Hamiltonians.
Phys. Lett. A 304 (2002), no. 3-4, 67--72.