The binding energy of ground state for hydrogenic impurity in multiple quantum dots is calculated in the framework of effective-mass approximation and using a variational method. It is shown that the binding energy is a function of the size of dots, impurity position and external fields strength. The binding energy has a maximum value when the impurity is located on the center of dots and decreases for other impurity positions. The external electric and magnetic fields change the magnitude and the position of peaks. PACS Codes 73.20.D; 71.21.La; 71.55.Eq

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Grating eliminated no-nonsense observation of ultrafast incident laser light e-fields is an experimental technique for the full characterization of ultrashort laser pulses. It requires the nonlinear conversion of broadband ultrashort optical pulses into their second harmonic generation (SHG) that is relatively tightly focused on a thick SHG crystal. In this paper, the laser focusing problem is experimentally presented and demonstrated in the measurements of 780 nm chirped pulses emitted from a Ti:sapphire oscillator. In this experimental study, it has been shown how the focusing effect can cause distortions in the trace of the chirped pulses. It is demonstrated that the measurement of broadband pulses requires that the beam have a wide angular divergence. Therefore, a tight focusing is essential. A long focal length leads to a smaller range of angles incident on the crystal causing an insufficient divergence angle. Finally, the ability of this device in the characterization of double and complicated chirped pulses is described. The broadening of complex chirped pulses after passing through a thick BK7 glass is measured and the group velocity dispersion of the BK7 glass is calculated as about 47.3 fs 2 mm −1 . Also the train of double chirped pulses created using a Michelson interferometer is measured and the spectral fringes marked by phase jumps are observed. The experimental results of the retrieved phases and intensities are in good agreement with independently measured data.

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