Coherent states are derived for one-dimensional systems generated by supersymmetry from an initial Hamiltonian with a purely discrete spectrum for which the levels depend analytically on their subindex. It is shown that the algebra of the initial system is inherited by its SUSY partners in the subspace associated to the isospectral part or the spectrum. The technique is applied to the harmonic oscillator, infinite well and trigonometric Pöschl-Teller potentials.

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We provide an explicit construction of entangled states in a noncommutative space with nonclassical states, particularly with the squeezed states. Noncommutative systems are found to be more entangled than the usual quantum mechanical systems. The noncommutative parameter provides an additional degree of freedom in the construction by which one can raise the entanglement of the noncommutative systems to fairly higher values beyond the usual systems. Despite of having classical-like behaviour, coherent states in noncommutative space produce little amount of entanglement and therefore they possess slight nonclassicality as well, which are not true for the coherent states of ordinary harmonic oscillator.

The method of symmetry reduction is used to solve Grassmann-valued differential equations. The (Nϭ2) supersymmetric Korteweg-de Vries equation is considered. It admits a Lie superalgebra of symmetries of dimension 5. A two-dimensional subsuperalgebra is chosen to reduce the number of independent variables in this equation. We are then able to give different types of exact solutions, in particular soliton solutions.

In this paper, we consider the one-dimensional anharmonic oscillator, which represents well the anharmonic vibrations in diatomic molecules. For the description of the associate potential we use the Morse potential, which gives a good approximation of the experimentally observed vibrational modes of molecules and hence contributes to the realistic description of the spectrum of diatomic molecules. The generalized and Gaussian coherent states are thus constructed and compared in terms of the localization of the particle in those states. We apply these results to the example of the sodium chloride molecule, 1H35Cl.

Transition of beam dynamics in waveguide arrays with commensurate Stark ladders Appl. Phys. Lett. 100, 041115 (2012) Two-bit quantum random number generator based on photon-number-resolving detection Rev. Sci. Instrum. 82, 073109 (2011) Decoherence and surface hopping: When can averaging over initial conditions help capture the effects of wave packet separation? J. Chem. Phys. 134, 244114 (2011) Photon counting statistics of single molecule in solid matrix JCP: BioChem.Using algebraic techniques, we realize a systematic search of different types of ladder operators for the Jaynes-Cummings model in the rotating-wave approximation. The link between our results and previous studies on the diagonalization of the associated Hamiltonian is established. Using some of the ladder operators obtained before, examples are given on the possibility of constructing a variety of interesting coherent states for this Hamiltonian.

Minimal electromagnetic coupling schemes entering into Klein–Gordon or Schrödinger equations are studied in connection with symmetries outside the symmetry groups of the corresponding free equations. The Schrader construction of the so-called (relativistic) Maxwell group is reviewed through group extensions of kinematical groups associated with (constant and uniform) electromagnetic fields. The construction of the Galilean (nonrelativistic) Maxwell group is given.