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The degeneracy associated with dynamical symmetry of a potential can be identified in quantum mechanics, by solving the Schrodinger equation analytically, using the method of separation of variables in at least two different coordinate systems, and in classical mechanics by solving the Hamilton-Jacobi equation. In the present pedagogical review, the notion of separability and superintegrability of a potential, with profound implications, is discussed. In an earlier tutorial paper, we addressed the [n.sup.2]-fold degeneracy of the hydrogen atom using the Casimir operators corresponding to the SO(4) symmetry of the 1/r potential. The present paper is a sequel to that work, in which we solve the Schrodinger equation for the hydrogen atom using separation of variables in the parabolic coordinate systems. In doing so, we take the opportunity to revisit some excellent works on symmetry and degeneracy in classical and quantum physics, if only to draw attention to these insightful studies, which unfortunately miss even a mention in most undergraduate and even graduate level courses in quantum mechanics and atomic physics. Key words: parabolic coordinates, accidental degeneracy, hydrogen atom symmetry, separability, integral of motion. La degenerescence associee a la symetrie dynamique du potentiel peut etre identifiee, en mecanique quantique par la solution de l'equation de Schrodinger analytiquement dans au moins deux systemes de coordonnees via la methode de separation des variables et en mecanique classique en solutionnant l'equation de Hamilton-Jacobi. Dans le present texte pedagogique, nous discutons les profondes implications de la separabilite et de la superintegrabilite d'un potentiel. Dans un tutoriel precedent, nous avons examine la degenerescence [n.sup.2] fois de l'atome d'hydrogene, en utilisant l'operateur de Casimir correspondant a la symetrie SO(4) du potentiel en 1/r. Le present article en est la suite, oU nous solutionnons l'equation de Schrodinger pour l'atome d'hydrogene dans le systeme des coordonnees paraboliques. Ce faisant, nous avons l'opportunite de revisiter certains excellents travaux sur la symetrie et la degenerescence en physique classique et quantique, ne serait-ce que pour attirer l'attention sur ces etudes eclairantes qui, malheureusement, ne sont meme pas mentionnees dans la plupart des cours de mecanique quantique et de physique atomique, tant au premier cycle qu'aux cycles avances. Mots-cles : coordonnees paraboliques, degenerescence accidentelle, symetrie de l'atone d'hydrogene, separabilite, integrale (premiere) de mouvement, constante du mouvement., 1. Introduction This paper is written as a sequel to an earlier tutorial article published by our group, 'The 'accidental' degeneracy of the hydrogen atom is no accident!' [1]. In [...]

High harmonic generation (HHG) from atoms near a plasmonic nanostructure interacting with a relatively low intensity driving laser field is a promising candidate for table top attosecond pulse source. The effect of carrier envelope phase (CEP) of the few cycle driving pulse on inhomogeneous high harmonics generation is well studied in literature, for example, the harmonic cut-off can be efficiently controlled by tuning the CEP. Here, we show selective enhancements of harmonic spectra due to half-cycle cutoff (HCO) which is highly sensitive to the CEP, in both spatially homogeneous and inhomogeneous driving laser fields. Essentially the selective enhancement of spectral structures results from contributions of both short and long trajectories in certain HCO regions. Compared to the homogeneous HHG in the presence of inhomogeneity, these enhanced groups eventually merge to the background with the increase of the strength of inhomogeneity. This limits the maximum possible tunability of selective enhancement. Further, near cut-off harmonics can be a good candidate to produce isolated attosecond pulses, with substantial control via CEP of the driving laser pulse along with the strength of inhomogeneity. [ABSTRACT FROM AUTHOR]