Subhash Saini

Semiclassical quantization by using the method of adiabatic switching of the perturbation: Fermi resonance

The method of adiabatic switching of perturbation is applied in semiclassical calculations of the eigenvalues of classically near‐integrable Hamiltonian describing a two‐dimensional coupled oscillator whose dynamics is dominated by an intrinsic 2:1 resonance. At low‐to‐intermediate excitations the semiclassical eigenvalues are generally in good agreement with quantum‐variational results. Even at high excitations, close to the classical escape energy, useful information on the location of quantal levels can be obtained. Limitations of the method are discussed.

A Model for motion in the chaotic regime: Classical and quantum viewpoints

Abstract A quantum theory of the magnetized hydrogen atom based on partitioning the space into physically important regions is given. Using known formalism, this partitioning supplies a fully quantal explanation of the effect of periodic orbits on the Fourier transforms of the spectra, scars in the wavefunctions, and level clustering. The formalism also leads to a simple non-periodic trajectory guided method to calculate quantum mechanically the Fourier peaks. The motion of the system is shown to be consistently that of a chaotic trajectory with segments of near periodic orbit-type motion.

Semi-classical eigenvalues using the classical Born-Oppenheimer adiabatic approximation

Abstract The classical Born-Oppenheimer method is applied to the two-degrees-of-freedom Henon-Heiles potential. The resulting one-dimensional potentials are then treated semi-classically to give the eigenvalues for the regular states. No trajectories are needed and the results are in good agreement with the exact results.

Semiclassical perturbation method based on the lie transform for multidimensional systems

Abstract A semiclassical perturbation method based on the Lie transform is used to calculate vibrational energy levels for multidimensional systems. No trajectories, initial searches, iterative procedures, Fourier analyses, or reference Hamiltonian searches are needed and the results are in good agreement with Einstein-Brillouin-Keller based methods.

Quasiclassical trajectory study of H2/LiF(001) corrugated surface scattering: Comparison with other theoretical results

Abstract The quasiclassical trajectory (QCT) method has been applied to treat the scattering of hydrogen from a LiF(001) surface in the energy range 0.5–0.9 eV. The influence of surface corrugation and collision energy on the main features of inelastic and elastic scattering are investigated. The results are compared with recent matrix-diagonalization sudden (MDS) calculations by Gerber et al. We also provide a test of the analytically-derived properties of the S -matrix found by Gerber et al. using the coordinate-representation sudden (CRS) method. The MDS and CRS results are broadly supported; however, a significant difference arises with respect to the importance of inelastic collisions as a function of energy. We have also compared the rotationally inelastic transition probabilities summed over all diffractive channels (QCT method) with the ones calculated using semiclassical perturbation (SCP) theory by Hubbard and Miller. Again, the major differences involve the energy dependence of the inelasticity. The energy dependence of the inelasticity found using the QCT method bears resemblance to the results of Adams, who treated the diatom-surface problem using the impulse-collision approximation (ICA).

On the quantisation of the two-dimensional harmonic oscillator with 2:1 resonance

Exact eigenfunctions, which simultaneously diagonalise the Hamiltonian of a 2:1 resonant, two-dimensional harmonic oscillator and an additional constant of the motion, cubic in the cartesian displacement coordinates and momenta, are found by direct solution of the Schrodinger equation in parabolic coordinates. The connection with the usual harmonic-oscillator cartesian basis is established and used in the formulation of a second-order perturbation theory for the oscillator with a particular form of nonlinear coupling. Uniform semiclassical quantisation of the unperturbed oscillator is discussed.