New approach to (quasi-)exactly solvable Schrödinger equations with a position-dependent effective mass (original) (raw)
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Effective mass schrödinger equation for exactly solvable class of one-dimensional potentials
Journal of Mathematical Chemistry, 2008
We deal with the exact solutions of Schrödinger equation characterized by positiondependent effective mass via point canonical transformations. The Morse, Pöschl-Teller and Hulthén type potentials are considered respectively. With the choice of position-dependent mass forms, exactly solvable target potentials are constructed. Their energy of the bound states and corresponding wavefunctions are determined exactly.
2006
Exact solutions of the Schrodinger equation are obtained for the Rosen-Morse and Scarf potentials with the position-dependent effective mass by appliying a general point canonical transformation. The general form of the point canonical transformation is introduced by using a free parameter. Two different forms of mass distributions are used. A set of the energy eigenvalues of the bound states and corresponding wave functions for target potentials are obtained as a function of the free parameter.
Effective mass schr�dinger equation for exactly solvable class of one-dimensional potentials
J Math Chem, 2008
We deal with the exact solutions of Schrodinger equation characterized by position-dependent effective mass via point canonical transformations. The Morse, Poschl-Teller and Hulthen type potentials are considered respectively. With the choice of position-dependent mass forms, exactly solvable target potentials are constructed. Their energy of the bound states and corresponding wavefunctions are determined exactly.
An exactly solvable Schrödinger equation with finite positive position-dependent effective mass
Journal of Mathematical Physics, 2010
The solution of the one-dimensional Schrödinger equation is discussed in the case of position-dependent mass. The general formalism is specified for potentials that are solvable in terms of generalized Laguerre polynomials and mass functions that are positive and bounded on the whole real x axis. The resulting four-parameter potential is shown to belong to the class of "implicit" potentials. Closed expressions are obtained for the bound-state energies and the corresponding wave functions, including their normalization constants. The constant mass case is obtained by a specific choice of the parameters. It is shown that this potential contains both the harmonic oscillator and the Morse potentials as two distinct limiting cases and that the original potential carries several characteristics of these two potentials. Possible generalizations of the method are outlined.
International Journal of Theoretical Physics, 2008
Exact solutions of the Schrödinger equation are obtained for the Rosen-Morse and Scarf potentials with the position-dependent effective mass by appliying a general point canonical transformation. The general form of the point canonical transformation is introduced by using a free parameter. Two different forms of mass distributions are used. A set of the energy eigenvalues of the bound states and corresponding wave functions for target potentials are obtained as a function of the free parameter.
A new class of quasi-exactly solvable potentials with a position-dependent mass
A new class of quasi exactly solvable potentials with a variable mass in the Schrödinger equation is presented. We have derived a general expression for the potentials also including Natanzon confluent potentials. The general solution of the Schrödinger equation is determined and the eigenstates are expressed in terms of the orthogonal polynomials.
A new class of quasi-exactly solvable potentials with position dependent mass
arXiv (Cornell University), 2004
A new class of quasi exactly solvable potentials with a variable mass in the Schrödinger equation is presented. We have derived a general expression for the potentials also including Natanzon confluent potentials. The general solution of the Schrödinger equation is determined and the eigenstates are expressed in terms of the orthogonal polynomials.
Analytic results in the position-dependent mass Schrodinger problem
Communications in Theoretical Physics
We investigate the Schrodinger equation for a particle with a nonuniform solitonic mass density. First, we discuss in extent the (nontrivial) position-dependent mass V (x) = 0 case whose solutions are hypergeometric functions in tanh 2 x. Then, we consider an external hyperbolic-tangent potential. We show that the effective quantum mechanical problem is given by a Heun class equation and find analytically an eigenbasis for the space of solutions. We also compute the eigenstates for a potential of the form V (x) = V0 sinh 2 x. *