A new shape invariance form of the trigonometric Scarf potential: Two-parameter cross-additivity shape invariance

Shape invariance and a universal form for the Gouy phase.

It is shown that Hermite-Gaussian beams, Laguerre-Gaussian beams, and certain linear combinations thereof are the only finite-energy coherent beams that propagate, on free propagation, in a shape-invariant manner. All shape-invariant beams have Gouy phase of the universal c arctan(z/zR) form, with quantized values for the prefactor c. It is also shown that, as limiting cases, even two- and thre...

Algebraic Approach to Shape Invariance

The integrability condition called shape invariance is shown to have an underlying algebraic structure and the associated Lie algebras are identified. These shape-invariance algebras transform the parameters of the potentials such as strength and range. Shape-invariance algebras, in general, are shown to be infinite-dimensional. The conditions under which they become finitedimensional are explo...

New exactly solvable Hamiltonians: Shape invariance and self-similarity.

Shape-invariance and Many-body Physics

Recent developments in the study of shape-invariant Hamiltonians are briefly summarized. Relations between certain exactly solvable problems in many-body physics and shape-invariance are explored. Connection between Gaudin algebras and supersymmet-ric quantum mechanics is pointed out.

Affine-permutation Symmetry: Invariance and Shape Space

Studying similarity of objects by looking at their shapes arises naturally in many applications. However, under different viewpoints one and the same object appears to have different shapes. In addition, the correspondence between their feature points are unknown to the viewer. In this paper, we introduce the concept of intrinsic shape of an object that is invariant to affine-permutation shape ...