The total and partial photodissociation cross sections of the molecular ion HeH + are computed by timedependent methods for fragmentation into the excited shells n =1,2,3 up to a photon energy of 40 eV. 1 ⌺ + and 1 ⌸ states are considered for parallel and perpendicular transitions for different initial rotational or vibrational excitations. Nonadiabatic radial and rotational couplings are taken into account. The results from coupledchannel equations are compared with the Born-Oppenheimer approximation. A time-dependent calculation with a femtosecond laser pulse is carried out to simulate a recent crossed beam photodissociation imaging experiment with vacuum ultraviolet free-electron laser ͓H. B. Pedersen et al., Phys. Rev. Lett. 98, 223202 ͑2007͔͒. The dominance of photodissociation perpendicular to the photon polarization is confirmed.

The charge transfer in low energy (0.25 to 150 eV/amu) H(nl) + He + (1s) collisions is investigated using a quasi-molecular approach for the n = 2, 3 as well as the first two n = 4 singlet states. The diabatic potential energy curves of the HeH + molecular ion are obtained from the adiabatic potential energy curves and the non-adiabatic radial coupling matrix elements using a two-by-two diabatization method, and a time-dependent wave-packet approach is used to calculate the stateto-state cross sections. We find a strong dependence of the charge transfer cross section in the principal and orbital quantum numbers n and l of the initial or final state. We estimate the effect of the non-adiabatic rotational couplings, which is found to be important even at energies below 1 eV/amu. However, the effect is small on the total cross sections at energies below 10 eV/amu. We observe that to calculate charge transfer cross sections in a n manifold, it is only necessary to include states with n ′ ≤ n, and we discuss the limitations of our approach as the number of states increases.

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Since the introduction of the concept of canonical coherent states (CS), associated with the one dimensional harmonic oscillator by Schrödinger in 1926 1 , followed decades in which this concept has reached great investigations 2 -5 . CS are a useful mathematical framework for dealing with the connection between classical and quantum mechanics 5-7 . These states can globally be constructed in three equivalent ways: (i) by defining them as eigenstates of the lowering operator (called CS of the Barut-Girardello 8 type), (ii) by applying a unitary displacement operator on a ground state (Klauder-Perelomov CS 9 or CS of the Gazeau-Klauder type), and (iii) by considering them as quantum states with a minimum uncertainty relationship 10,11 .The CS for shape-invariant potentials (SIP) performed in this work 12,13 , belong to the Barut-Girardello type. They are built using algebraic approach based on the supersymmetric quantum mechanics (SUSY-QM) 14,15 . SUSY QM deals with the study of partner Hamiltonians which are isospectral, that is, they have almost the same energy eigenvalues. A number of such partner Hamiltonians satisfy an integrability condition called shape invariance 16 -18 .However, not all exactly solvable systems are shape-invariant.Recently, a considerable attention is devoted to photon-added CS (PACS) 19 -22 , first introduced by Agarwal and Tara 23 . The PACS represent interesting states generalizing both the Fock states and CS. Indeed, they are obtained by repeatedly operating the photon creation operator on an ordinary CS. In some previous works, the PACS were assimilated to nonlinear CS. Their various generalizations were also performed 24,25 . They evidence some nonclassical effects, for e.g, amplitude squeezing, sub-Poissonian behaviour, nonclassical quasi-probability distribution. In one of our previous papers 26 , a family of photon added as well as photon depleted CS related to the inverse of ladder operators acting on hypergeometric CS was introduced. Their squeezing and antibunching properties were investigated in both standard (nondeformed) and deformed quantum optics. Recently 27 , new generalized PACS were formulated by excitations on a family of generalized CS. Their non-classical features and quantum statistical properties were compared with those obtained by Agarwal. Besides, in another paper 28 , photon-subtracted generalized CS, which are reminiscent of the PACS, were introduced; their nonclassical features were also discussed. PACS find many applications in physics. In 29 , a generating Schrödinger-cat-like states of a single-mode

This work gives value to the importance of Hilbert-Schmidt operators in the formulation of noncommutative quantum theory. A system of charged particle in a constant magnetic field is investigated in this framework.

This paper presents the construction of a new set of generalized photonadded coherent states related to associated hypergeometric functions introduced in our previous work (Hounkonnou M N and Sodoga K 2005 J. Phys. A: Math. Gen 38 7851). These states satisfy all required mathematical and physical properties. The associated Stieltjes power-moment problem is explicitly solved by using Meijer's G-function and the Mellin inversion theorem. Relevant quantum optical and thermal characteristics are investigated. The formalism is applied to particular cases of the associated Hermite, Laguerre, Jacobi polynomials and hypergeometric functions. Their corresponding states exhibit sub-Poissonian photon number statistics.