The O(4) symmentry of hydrogenic atoms is used to interpret angular momentum nlm and Stark [vertical line] n 1 n 2 m eigenstates as different realizations of irreducible representations of the O(4) group Differential expressions are obtained for [vertical line] n 1 n 2 m shift operators, and for the [vertical line] nlm shift operator O - 1 which changes l and m by -1 These are used to obtain the formula < n 1 n 2 m | nlm '> = (-1) 2 n 2 +| m |- m 2 C [1/2( n -1), 1/2( n -1), l , 1/2( m + n 2 - n 1 ), 1/2( m + n 1 - n 2 ), m '] for the transformation matrix elements connecting the two sets of states where, in the notation of Rose, C ( J 1 J 2 J , m 1 m 2 m ) is the angular momentum Clebsch-Gordan coefficientThe O(4) symmentry of hydrogenic atoms is used to interpret angular momentum nlm and Stark [vertical line] n 1 n 2 m eigenstates as different realizations of irreducible representations of the O(4) group Differential expressions are obtained for [vertical line] n 1 n 2 m shift operators, and for the [vertical line] nlm shift operator O - 1 which changes l and m by -1 These are used to obtain the formula < n 1 n 2 m | nlm '> = (-1) 2 n 2 +| m |- m 2 C [1/2( n -1), 1/2( n -1), l , 1/2( m + n 2 - n 1 ), 1/2( m + n 1 - n 2 ), m '] for the transformation matrix elements connecting the two sets of states where, in the notation of Rose, C ( J 1 J 2 J , m 1 m 2 m ) is the angular momentum Clebsch-Gordan coefficient

Proceedings of the Physical SocietyAug 1, 196791 citations

On a hydrogen atom

L. Stupelis

Lithuanian Mathematical JournalJan 1, 20070 citations

Luttinger liquid and charge density wave phases in a spinless fermion wire on a semiconducting substrate

Anas Abdelwahab, Eric Jeckelmann

An interacting spinless fermion wire coupled to a three-dimensional (3D) semiconducting substrate is approximated by a narrow ladder model (NLM) with varying number of legs. We compute density distributions, gaps, charge density wave (CDW) order parameters, correlation functions, and the central charge using the density-matrix renormalization group method. Three ground-state phases are observed: a one-component Luttinger liquid, a quasi-one-dimensional (1D) CDW insulator, and a band insulator. We investigated the convergence of the NLM properties with increasing number of legs systematically and confirm that the NLM is a good approximation for the quasi-1D phases (Luttinger liquid and CDW) of the 3D wire-substrate model. The quantum phase transitions between these phases are investigated as function of the coupling between wire and substrate. The critical nearest-neighbor interaction increases with increasing coupling between wire and substrate and thus the substrate stabilizes the Luttinger liquid in the wire. Our study confirms that a Luttinger liquid or CDW insulator phase could occur in the low-energy properties of atomic wires deposited on semiconducting substrates.An interacting spinless fermion wire coupled to a three-dimensional (3D) semiconducting substrate is approximated by a narrow ladder model (NLM) with varying number of legs. We compute density distributions, gaps, charge density wave (CDW) order parameters, correlation functions, and the central charge using the density-matrix renormalization group method. Three ground-state phases are observed: a one-component Luttinger liquid, a quasi-one-dimensional (1D) CDW insulator, and a band insulator. We investigated the convergence of the NLM properties with increasing number of legs systematically and confirm that the NLM is a good approximation for the quasi-1D phases (Luttinger liquid and CDW) of the 3D wire-substrate model. The quantum phase transitions between these phases are investigated as function of the coupling between wire and substrate. The critical nearest-neighbor interaction increases with increasing coupling between wire and substrate and thus the substrate stabilizes the Luttinger liquid in the wire. Our study confirms that a Luttinger liquid or CDW insulator phase could occur in the low-energy properties of atomic wires deposited on semiconducting substrates.

arXiv:1810.02190Physical review. B./Physical review. BDec 18, 20185 citations

Free-bound dipole transition in H-like atoms

Nadia Mezincescu, C. Vrejoiu

Physics Letters AJun 1, 19930 citations

Classical and quantal atomic form factors for nlm→n′l′m transitions

M. Raymond Flannery, D. Vrinceanu

An analytical expression for the classical form factor or impulsive probability ${P}_{\mathrm{if}}(\mathbf{q})$ for $\mathrm{nl}\stackrel{\ensuremath{\rightarrow}}{m}{n}^{\ensuremath{'}}{l}^{\ensuremath{'}}m$ transitions is derived directly from the ``phase-space distribution'' method [Phys. Rev. A 60, 1053 (1999)] and is compared with quantal results. Exact universal scaling laws are derived for the classical probability for any $\stackrel{\ensuremath{\rightarrow}}{i}f$ transition. As n is increased, convergence of the quantal to classical results is obtained and it becomes even more rapid upon averaging in succession over the m and then the $\mathit{l}$ substates. The classical results reveal the basic reason for the underlying structure in the variation of ${P}_{\mathrm{if}}$ with momentum transfer $\mathbf{q}.$ Classical form factors can operate as an effective averaged version of the exact quantal counterpart.An analytical expression for the classical form factor or impulsive probability ${P}_{\mathrm{if}}(\mathbf{q})$ for $\mathrm{nl}\stackrel{\ensuremath{\rightarrow}}{m}{n}^{\ensuremath{'}}{l}^{\ensuremath{'}}m$ transitions is derived directly from the ``phase-space distribution'' method [Phys. Rev. A 60, 1053 (1999)] and is compared with quantal results. Exact universal scaling laws are derived for the classical probability for any $\stackrel{\ensuremath{\rightarrow}}{i}f$ transition. As n is increased, convergence of the quantal to classical results is obtained and it becomes even more rapid upon averaging in succession over the m and then the $\mathit{l}$ substates. The classical results reveal the basic reason for the underlying structure in the variation of ${P}_{\mathrm{if}}$ with momentum transfer $\mathbf{q}.$ Classical form factors can operate as an effective averaged version of the exact quantal counterpart.

Physical Review AJan 4, 20025 citations

An analytical expression for the classical form factor or impulsive probability

{P}_{\mathrm{if}}(\mathbf{q})

for $\mathrm{nl}\stackrel{\ensuremath{\rightarrow}}{m}{n}^{\ensuremath{'}}{l}^{\ensuremath{'}}m$ transitions is derived directly from the ``phase-space distribution'' method [Phys. Rev. A 60, 1053 (1999)] and is compared with quantal results. Exact universal scaling laws are derived for the classical probability for any $\stackrel{\ensuremath{\rightarrow}}{i}f$ transition. As n is increased, convergence of the quantal to classical results is obtained and it becomes even more rapid upon averaging in succession over the m and then the

\mathit{l}

substates. The classical results reveal the basic reason for the underlying structure in the variation of

{P}_{\mathrm{if}}

with momentum transfer

\mathbf{q}.

Classical form factors can operate as an effective averaged version of the exact quantal counterpart.