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Register a new userExact solution of Effective mass Schrodinger Equation for the Hulthen potential
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A general form of the effective mass Schrodinger equation is solved exactly for Hulthen potential. Nikiforov-Uvarov method is used to obtain energy eigenvalues and the corresponding wave functions. A free parameter is used in the transformation of the wave function.
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The Schr{o}dinger equation is solved exactly for some well known potentials. Solutions are obtained reducing the Schr{o}dinger equation into a second order differential equation by using an appropriate coordinate transformation. The Nikiforov-Uvarov method is used in the calculations to get energy eigenvalues and the corresponding wave functions.
The Dirac equation, with position-dependent mass, is solved approximately for the generalized Hulth{e}n potential with any spin-orbit quantum number $kappa$. Solutions are obtained by using an appropriate coordinate transformation, reducing the effective mass Dirac equation to a Schr{o}dinger-like differential equation. The Nikiforov-Uvarov method is used in the calculations to obtain energy eigenvalues and the corresponding wave functions. Numerical results are compared with those given in the literature. Analytical results are also obtained for the case of constant mass and the results are in good agreement with the literature.
Effective mass Schrodinger equation is solved exactly for a given potential. Nikiforov-Uvarov method is used to obtain energy eigenvalues and the corresponding wave functions. A free parameter is used in the transformation of the wave function. The effective mass Schrodinger equation is also solved for the Morse potential transforming to the constant mass Schr{o}dinger equation for a potential. One can also get solution of the effective mass Schrodinger equation starting from the constant mass Schrodinger equation.
We solve rigorously the time dependent Schrodinger equation describing electron emission from a metal surface by a laser field perpendicular to the surface. We consider the system to be one-dimensional, with the half-line $x<0$ corresponding to the bulk of the metal and $x>0$ to the vacuum. The laser field is modeled as a classical electric field oscillating with frequency $omega$, acting only at $x>0$. We consider an initial condition which is a stationary state of the system without a field, and, at time $t=0$, the field is switched on. We prove the existence of a solution $psi(x,t)$ of the Schrodinger equation for $t>0$, and compute the surface current. The current exhibits a complex oscillatory behavior, which is not captured by the simple three step scenario. As $ttoinfty$, $psi(x,t)$ converges with a rate $t^{-frac32}$ to a time periodic function with period $frac{2pi}{omega}$ which coincides with that found by Faisal, Kaminski and Saczuk (Phys Rev A 72, 023412, 2015). However, for realistic values of the parameters, we have found that it can take quite a long time (over 50 laser periods) for the system to converge to its asymptote. Of particular physical importance is the current averaged over a laser period $frac{2pi}omega$, which exhibits a dramatic increase when $hbaromega$ becomes larger than the work function of the metal, which is consistent with the original photoelectric effect.
Exact solutions of effective radial Schr{o}dinger equation are obtained for some inverse potentials by using the point canonical transformation. The energy eigenvalues and the corresponding wave functions are calculated by using a set of mass distributions
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