Complex scaling method

Figure 4.2 demonstrates the instanton trajectories at different temperatures for C = 0.5, fl = 0.5, n = 2. For temperatures close to the Tc the trajectory runs near the saddle point, and it deviates from the saddle point with increasing fi. The Hamiltonian (4.29) with n = 1 has recently been studied numerically within the complex scaling method [Hontscha et al. 1990]. Using these data we can estimate the accuracy of the instanton... 

N. Elander, E. Yarevsky, Exterior complex scaling method applied to doubly excited states of helium, Phys. Rev. A. 57 (1998) 3119. 

Numerical Application of the Complex Scaling Method in the Hartree-Fock Approximation. 

Figure 1. Complex energy levels for a model ICl-Ne system (in reduced units). Shown are the accurate results (complex scaling method, crosses), first-order diahatic (FOD, fdled squares) and first-order adiabatic (FOA. open circles).

Complex Scaling Method for Numerical and Piecewise Potentials... 

The complex coordinate rotation (CCR) or complex scaling method (5,6,10,19) is directly based on the ABCS theory (1-3), therefore Reinhardt (5) also called it the direct approach. A complex rotated Hamiltonian, H 0), is obtained from the electron Hamiltonian of the atom, H, by replacing the radial coordinates r by re, where 0 is a real parameter. The eigenproblem of this non-Hermitian operator is solved variationally in a basis of square-integrable functions. The matrix representation of H ) is obtained by simple scaling of matrices T and V representing the kinetic and Coulomb potential part of the unrotated Hamiltonian H,... 

The characteristics developed here emanate from the so-called complex scaling method [11] of atomic and molecular physics [14, 15], The observance to incorporate complex symmetric interactions in effect provides for transitions from specific quantum non-local representations to classical locality. 

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