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Register a new userCoherent states of the two-dimensional non-separable supersymmetric Morse potential
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Supersymmetry is a technique that allows us to extract information about the states and spectra of quantum mechanical systems which may otherwise be unsolvable. In this paper we reconstruct Ioffes set of states for the singular non-separable two-dimensional Morse potential using supersymmetry from a non-degenerate set of states constructed for the initial separable Morse Hamiltonian. We define generalised coherent states, compute their uncertainty relations, and we find that the singularity in the partner Hamiltonian significantly affects the localisation of the coherent state wavefunction.
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In this paper we construct coherent states for the two-dimensional Morse potential. We find the dependence of the spectrum on the physical parameters and use this to understand the emergence of accidental degeneracies. It is observed that, under certain conditions pertaining to the irrationality of the parameters, accidental degeneracies do not appear and as such energy levels are at most two-fold degenerate. After defining a non-degenerate spectrum and set of states for the 2D Morse potential, we construct generalised coherent states and discuss the spatial distribution of their probability densities and their uncertainty relations.
The complex scaling method is applied to study the resonances of a Dirac particle in a Morse potential. The applicability of the method is demonstrated with the results compared with the available data. It is shown that the present calculations in the nonrelativistic limit are in excellent agreement with the nonrelativistic calculations. Further, the dependence of the resonant parameters on the shape of the potential is checked, and the unusual sensitivity to the potential parameters is revealed. By comparing the energies and widths of the pseudospin doublets, well pseudospin symmetry is discovered in the present model. The relationship between the pseudospin symmetry and the shape of the potential is investigated by changing the Morse potential shaped by the dissociation energy, the equilibrium intermolecular distance, and the positive number controlling the decay length of the potential.
Path integral solutions are obtained for the the PT-/non-PT-Symmetric and non-Hermitian Morse Potential. Energy eigenvalues and the corresponding wave functions are obtained.
The one-dimensional effective-mass Klein-Gordon equation for the real, and non-textrm{PT}-symmetric/non-Hermitian generalized Morse potential is solved by taking a series expansion for the wave function. The energy eigenvalues, and the corresponding eigenfunctions are obtained. They are also calculated for the constant mass case.
Two-photon states entangled in continuous variables such as wavevector or frequency represent a powerful resource for quantum information protocols in higher-dimensional Hilbert spaces. At the same time, there is a problem of addressing separately the corresponding Schmidt modes. We propose a method of engineering two-photon spectral amplitude in such a way that it contains several non-overlapping Schmidt modes, each of which can be filtered losslessly. The method is based on spontaneous parametric down-conversion (SPDC) pumped by radiation with a comb-like spectrum. There are many ways of producing such a spectrum; here we consider the simplest one, namely passing the pump beam through a Fabry-Perot interferometer. For the two-photon spectral amplitude (TPSA) to consist of non-overlapping Schmidt modes, the crystal dispersion dependence, the length of the crystal, the Fabry-Perot free spectral range and its finesse should satisfy certain conditions. We experimentally demonstrate the control of TPSA through these parameters. We also discuss a possibility to realize a similar situation using cavity-based SPDC.
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