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Register a new userExact Solutions of Effective-Mass Dirac-Pauli Equation with an Electromagnetic Field
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The exact bound state solutions of the Dirac-Pauli equation are studied for an appropriate position-dependent mass function by using the Nikiforov-Uvarov method. For a central electric field having a shifted inverse linear term, all two kinds of solutions for bound states are obtained in closed forms.
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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.
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.
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.
We consider Yukawa theory in which the fermion mass is induced by a Higgs like scalar. In our model the fermion mass exhibits a temporal dependence, which naturally occurs in the early Universe setting. Assuming that the complex fermion mass changes as a tanh-kink, we construct an exact, helicity conserving, CP-violating solution for the positive and negative frequency fermionic mode functions, which is valid both in the case of weak and strong CP violation. Using this solution we then study the fermionic currents both in the initial vacuum and finite density/temperature setting. Our result shows that, due to a potentially large state squeezing, fermionic currents can exhibit a large oscillatory magnification. Having in mind applications to electroweak baryogenesis, we then compare our exact results with those obtained in a gradient approximation. Even though the gradient approximation does not capture the oscillatory effects of squeezing, it describes quite well the averaged current, obtained by performing a mode sum. Our main conclusion is: while the agreement with the semiclassical force is quite good in the thick wall regime, the difference is sufficiently significant to motivate a more detailed quantitative study of baryogenesis sources in the thin wall regime in more realistic settings.
The Dirac-Morse problem are investigated within the framework of an approximation to the term proportional to $1/r^2$ in the view of the position-dependent mass formalism. The energy eigenvalues and corresponding wave functions are obtained by using the parametric generalization of the Nikiforov-Uvarov method for any $kappa$-value. It is also studied the approximate energy eigenvalues, and corresponding wave functions in the case of the constant-mass for pseudospin, and spin cases, respectively.
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