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

Lui, Wayne W.; Fukuma, Masao
September 1986
Journal of Applied Physics;9/1/1986, Vol. 60 Issue 5, p1555
Academic Journal
Describes an exact method of solving the Schrodinger equation across an arbitrary one-dimensional piecewise-linear potential. Derivation of the calculation algorithm; Applications employing the algorithm; Determination of eigenenergies for a particular potential wall.


Related Articles

  • Approximate Analytical Solution of the Schrödinger 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 Schrödinger 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...

  • Schrödinger 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 Schrödinger operators H = −Δ + 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 deformed Schrödinger equation with a class of non-central physical potentials. Chabab, M.; El Batoul, A.; Oulne, M. // Journal of Mathematical Physics;2015, Vol. 56 Issue 6, p1 

    In this paper, we present exact solutions of Schrödinger equation for a class of non-central physical potentials within the formalism of position-dependent effective mass. The energy eigenvalues and eigenfunctions of the bound-states for the Schrödinger equation are obtained analytically...

  • Exact solutions of the Schrödinger 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...

  • Energy eigenfunctions for position-dependent mass particles in a new class of molecular Hamiltonians. Christiansen, H. R.; Cunha, M. S. // Journal of Mathematical Physics;2014, Vol. 55 Issue 9, p1 

    Based on recent results on quasi-exactly solvable Schrodinger equations, we review a new phenomenological potential class lately reported. In the present paper, we consider the quantum differential equations resulting from position-dependent mass (PDM) particles. We first focus on the PDM...

  • Exact solutions of the Schrödinger 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 Schrödinger 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 SCHRÖDINGER 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 Schrödinger equation -ΔΨ(r)+V (r)Ψ(r) = EΨ(r) in N spatial dimensions. Based on this proposed criteria, we prove a new comparison theorem in quantum...

  • 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...

  • 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...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics