New hydrogen-like potentials

Using the modified factorization method introduced by Mielnik, we construct a new class of radial potentials whose spectrum for l=0 coincides exactly with that of the hydrogen atom. A limiting case of our family coincides with the potentials previously derived by Abraham and MosesComment: 6 pages, latex, 2 Postscript figure

Evidence for a phenomenological supersymmetry in atomic physics

We show that supersymmetric quantum mechanics may be used to interrelate the spectra of different atoms and ions. This supersymmetry is broken by electron-electron interactions

Reply to "Comment on 'Analytical wave functions for atomic quantum-defect theory'"

The preceding paper, by Martin and Barrientos [Phys. Rev. A 43, 4061 (1991)], comments on our supersymmetry-inspired model of atomic physics. We relate this to other Comments [Rau, Phys. Rev. Lett. 56, 95 (1986) and Goodfriend, Phys. Rev. A 41, 1730 (1990)] and point out that, although the mathematics and physics of the 1974 Simons model [J. Chem. Phys. 60, 645 (1974)] is similar to ours, it is not identical. This is elucidated by explicitly comparing our symmetry-based approach to the more phenomenological approach of Martin and Barrientos

Evidence from alkali-metal-atom transition probabilities for a phenomenological atomic supersymmetry

We review the proposal that relationships between physical spectra of certain atoms can be considered as evidence for a phenomenological supersymmetry. Next, a comparison is made between the supersymmetric and the hydrogenic approximations. We then present the calculation of low-Z alkali-metal-atom transition probabilities between low-n states, using supersymmetric wave functions. These probabilities agree more closely with accepted values than do those obtained with use of the hydrogenic approximation. This shows that, in simple radial Schrödinger theory, supersymmetry is a concept providing insight into the true, fermionic, many-body physics of these atoms

Analytical wave functions for atomic quantum-defect theory

We present an exactly solvable effective potential that reproduces atomic spectra in the limit of exact quantum-defect theory, i.e., the limit in which, for a fixed l, the principal quantum number is modified by a constant: $n^*=\text{n}-\delta (\text{l})$. Transition probabilities for alkali atoms are calculated using the analytical wave functions obtained and agree well with accepted values. This allows us to make phenomenological predictions for certain unknown transition probabilities. Our analytical wave functions might serve as useful trial wave functions for detailed calculations

s-wave scattering and the zero-range limit of the finite square well in arbitrary dimensions

We examine the zero-range limit of the finite square well in arbitrary dimensions through a systematic analysis of the reduced, s-wave two-body time-independent Schr\"odinger equation. A natural consequence of our investigation is the requirement of a delta-function multiplied by a regularization operator to model the zero-range limit of the finite-square well when the dimensionality is greater than one. The case of two dimensions turns out to be surprisingly subtle, and needs to be treated separately from all other dimensions

Reply to "Comment on 'Fine-structure and analytical quantum-defect wave functions'"

The preceding Comment by Goodfriend [Phys. Rev. A 41, 1730 (1990)] contains three criticisms of our model for analytical quantum-defect wave functions vis-á-vis the atomic Fues potential of Simons [J. Phys. Chem. 55, 756 (1971)]. We rebut the first two criticisms explicitly. This makes the third criticism moot. We stand by our result

Fine structure and analytical quantum-defect wave functions

We investigate the domain of validity of previously proposed analytical wave functions for atomic quantum-defect theory. This is done by considering the fine-structure splitting of alkali-metal and singly ionized alkaline-earth atoms. The Landé formula is found to be naturally incorporated. A supersymmetric-type integer is necessary for finite results. Calculated splittings correctly reproduce the principal features of experimental values for alkali-like atoms

Supercoherent states

A general approach is presented for constructing coherent states for supersymmetric systems. It uses Rogers's supermanifold formulation of supergroups to extend the group-theoretic method. Supercoherent states are explicitly obtained for the supersymmetric harmonic oscillator. They are shown to be eigenstates of the supersymmetric annihilation operator and to be minimum-uncertainty states. Two more-complex situations with extended physical supersymmetries are also considered: an electron moving in a constant magnetic field, and the electron-monopole system. The supercoherent states for these systems are found using super Baker-Campbell-Hausdorff relations and their interpretation is elucidated

Complexity, Tunneling and Geometrical Symmetry

It is demonstrated in the context of the simple one-dimensional example of a barrier in an infinite well, that highly complex behavior of the time evolution of a wave function is associated with the almost degeneracy of levels in the process of tunneling. Degenerate conditions are obtained by shifting the position of the barrier. The complexity strength depends on the number of almost degenerate levels which depend on geometrical symmetry. The presence of complex behavior is studied to establish correlation with spectral degeneracy.Comment: 9 revtex pages, 6 Postscript figures (uuencoded