# Exact solution of the Schrodinger equation across an arbitrary one-dimensional piecewise-linear potential barrier

## Related Articles

- Approximate Analytical Solution of the SchrÃ¶dinger Equation with the Hulthen Potential for Arbitrary L-State. Ikot, Akpan N.; Akpabio, Louis E. // International Review of Physics;Aug2010, Vol. 4 Issue 4, p224
We solve the radial SchrÃ¶dinger equation with Hulthen potential analytically. Using the Nikiforov -- Uvarov method, we obtained the eigenvalues and eigenfunctions of the Hulthen potential with the negative energy levels for an arbitrary l-state where the centrifugal potential was approximated...

- SchrÃ¶dinger Dispersive Estimates for a Scaling-Critical Class of Potentials. Beceanu, Marius; Goldberg, Michael // Communications in Mathematical Physics;Sep2012, Vol. 314 Issue 2, p471
We prove a dispersive estimate for the evolution of SchrÃ¶dinger operators H = âˆ’Î” + V( x) in $${{\mathbb R}^3}$$ . The potential should belong to the closure of $${C^c_b(\mathbb{R}^3)}$$ with respect to the global Kato norm. Some additional spectral conditions are imposed, namely...

- Exact solutions of the SchrÃ¶dinger equation with position dependent mass for the solvable potentials. Aricak, F.; Sezgin, M. // AIP Conference Proceedings;8/10/2012, Vol. 1470 Issue 1, p148
In this work the infinitesimal operators of the regular representations of the group SL(R, 2) are considered. According to these infinitesimal operators the Casimir operator is expressed. The Hamiltonian H is related to Casimir operator C of the group. The energy eigenvalues and the...

- Exact solutions of the SchrÃ¶dinger equation via Laplace transform approach: pseudoharmonic potential and Mie-type potentials. Arda, Altuğ; Sever, Ramazan // Journal of Mathematical Chemistry;Apr2012, Vol. 50 Issue 4, p971
Exact bound state solutions and corresponding normalized eigenfunctions of the radial SchrÃ¶dinger equation are studied for the pseudoharmonic and Mie-type potentials by using the Laplace transform approach. The analytical results are obtained and seen that they are the same with the ones...

- SPECTRAL BISECTION ALGORITHM FOR SOLVING SCHRÃ–DINGER EQUATION USING UPPER AND LOWER SOLUTIONS. Katatbeh, Qutaibeh Deeb // Electronic Journal of Differential Equations;2007, Vol. 2007, p1
This paper establishes a new criteria for obtaining a sequence of upper and lower bounds for the ground state eigenvalue of SchrÃ¶dinger equation -Î”Î¨(r)+V (r)Î¨(r) = EÎ¨(r) in N spatial dimensions. Based on this proposed criteria, we prove a new comparison theorem in quantum...

- On the Schrodinger equation with steplike potentials. Aktosun, Tuncay // Journal of Mathematical Physics;Nov99, Vol. 40 Issue 11, p5289
Studies a Schrodinger equation with potentials asymptotic to a positive constant on the right half line in a certain sense. Derivation of the zero-energy limits of the scattering coefficients (SC); Mathematical representations of the SC for the potential; Number of bound states for the two...

- Small-energy asymptotics of the scattering matrix for the matrix SchroÂ¨dinger equation on the line. Aktosun, Tuncay; Klaus, Martin; van der Mee, Cornelis // Journal of Mathematical Physics;Oct2001, Vol. 42 Issue 10
The one-dimensional matrix SchroÂ¨dinger equation is considered when the matrix potential is self-adjoint with entries that are integrable and have finite first moments. The small-energy asymptotics of the scattering coefficients are derived, and the continuity of the scattering coefficients...

- The removal of an energy dependence from the interaction in two-body systems. Motovilov, A. K. // Journal of Mathematical Physics;Dec91, Vol. 32 Issue 12, p3509
Energy-independent potentials that are almost spectrally equivalent to the energy-dependent ones are constructed. A case of polar energy dependence is studied especially. A profound connection between the energy-independent potentials existence and a spectral problem for the initial...

- Schrï¿½dinger equation for convex plane polygons: A tiling method for the derivation of eigenvalues and eigenfunctions. Amar, V.; Pauri, M.; Scotti, A. // Journal of Mathematical Physics;Sep91, Vol. 32 Issue 9, p2442
Motivated by a recently advanced conjecture on the ergodic properties of Quantum Systems, the problem of solving the Schrï¿½dinger equation for a free particle in a plane polygonal enclosure is revisited. It will be shown that two elementary lemmas suffice to give a complete characterization...