Complex Coordinate Scaling and the Schrödinger Equation
2018-01-22
Relativity and Gravity Publication - No. 30
Buenker
Robert J.
Prof. Dr.
Buenker, Robert J.
aut
en
<p> The complex rotation method (CRM) for the description of quantum mechanical resonance states
is critically analyzed by noting that quantum mechanical eigenvalues are not affected by a change
In spatial coordinates. On this basis it is concluded that equivalent solutions of the Schrödinger
equation for a complex-rotated Hamiltonian H (θ) can be obtained without loss of accuracy by
uslng the un-rotated Hamiltonian H (0) in its place. Despite the fact that the latter operator is
hermitean, it is possible to obtain a complex symmetric matrix representation for it by following
a few simple rules: a) the square-integrable basis functions must have complex exponents, i.e.
with non-zero imaginary components, and b) the symmetric scalar product must be employed to
compute matrix elements of H (0). The nature of this approximation is investigated by means of
explicit calculations which are based on diabatic RKR potentials for the B <sup>1</sup>Σ<sup>+</sup> - D' <sup>1</sup>Σ<sup>+</sup> vibronic
resonance states of the CO molecule.
2018-01-22T10:45:48.961Z
2018-01-22T11:42:32.365Z
published
Pub