Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Open Physics

Solutions of the Schrödinger equation for Dirac delta decorated linear potential

Haydar Uncu, Hakan Erkol, Ersan Demiralp, Haluk Beker

Published Jun 1, 2005• 7 citations
Publisher

Abstract

Abstract We have studied bound states of the Schrödinger equation for a linear potential together with any finite number (P) of Dirac delta functions. Forx where 0f; 0x 1x 2x P , theσ i are arbitrary real numbers, and the potential is infinite forx
DOI
10.2478/bf02475594

Related papers

Bound state solutions of the Schrödinger equation for a -symmetric potential with Dirac delta functions

Haydar Uncu, Ersan Demiralp

Physics Letters A•Jun 23, 2006•16 citations

Bound states ofn-dimensional harmonic oscillator decorated with Dirac delta functions

Ersan Demiralp

Bound state solutions of the Schrödinger equation have been investigated for n -dimensional ( n ⩾ 2) harmonic oscillator potential decorated with any finite number ( P ) of Dirac delta functions. The potential is radially symmetric and given as , where σ i s are arbitrary real numbers, r 1 < r 2 < ⋅⋅⋅ < r P and r i ∊ (0, + ∞). We have demonstrated that addition of Dirac delta functions lifts the accidental degeneracies of n -dimensional harmonic oscillator energy levels and leaves only the degeneracy due to the radial symmetry. Explicit forms of bound state eigenfunctions and the eigenvalue equation are given for n , l values, where n is the space dimension and l is the degree of n -dimensional spherical harmonics. We have shown that, for given n and l , there are a countably infinite number of bound state energy levels which are continuous functions of ω, σ i s and at most P of them can be negative.

Journal of Physics A Mathematical and General•May 18, 2005•29 citations

The One-Dimensional Schrödinger Equation; Bound States

Rocco Schiavilla

Bound states in one-dimensional finite and infinite wells and delta-function potentials, and combinations of these, are obtained; the WKB method for bound states is introduced; the consequences of a parity-invariant potential for the eigenfunctions are derived.

Cambridge University Press eBooks•Dec 5, 2024•0 citations

Simple exact solution of the one-dimensional Schrödinger equation with continuous plus δ -function potentials of arbitrary position and strength

J. Ronald Farias

A simple exact solution of a one-dimensional Schr\"odinger equation which describes the motion of a particle in a continuous potential $V(x)$ and scattering from a finite set of $\ensuremath{\delta}$-function potentials of arbitrary positions and strengths is found.

Physical Review A•Aug 1, 1980•4 citations

A Particle Interacting with V-shaped Potential Decorated by a Dirac Delta Function Interaction at Center

Wang Xin, Tang Liang-Hui, Wu Reng-Lai +2 more

The Schrödinger equation for a particle in the V-shaped potential decorated by a repulsive or attractive Dirac delta function interaction at the center is solved, demonstrating the crucial influence of point interaction on the even-parity states of the original system without decoration. As strength of the attraction increases, the ground state energy falls down without limit; and in limit of infinitely large attraction, the ground state approaches a singular state. Our analysis and conclusion can be readily generalized to any one-dimensional system a particle interacts with symmetrical potential plus the Dirac delta function interaction at the center.

Communications in Theoretical Physics•Feb 1, 2010•5 citations

Supersymmetric quantum mechanics: Examples with dirac δ functions

J. Goldstein, C. Lebiedzik, Richard W. Robinett

We examine the bound-state spectra of several one-dimensional supersymmetric quantum mechanical systems containing Dirac δ-function potentials. Specifically, we investigate the cases of two attractive δ functions, as well as both the infinite well and simple harmonic potentials with an added attractive or repulsive δ function.

American Journal of Physics•Jul 1, 1994•16 citations
Bound state solutions of the Schrödinger equation have been investigated for n -dimensional ( n ⩾ 2) harmonic oscillator potential decorated with any finite number ( P ) of Dirac delta functions. The potential is radially symmetric and given as , where σ i s are arbitrary real numbers, r 1 < r 2 < ⋅⋅⋅ < r P and r i ∊ (0, + ∞). We have demonstrated that addition of Dirac delta functions lifts the accidental degeneracies of n -dimensional harmonic oscillator energy levels and leaves only the degeneracy due to the radial symmetry. Explicit forms of bound state eigenfunctions and the eigenvalue equation are given for n , l values, where n is the space dimension and l is the degree of n -dimensional spherical harmonics. We have shown that, for given n and l , there are a countably infinite number of bound state energy levels which are continuous functions of ω, σ i s and at most P of them can be negative.
A simple exact solution of a one-dimensional Schr\"odinger equation which describes the motion of a particle in a continuous potential V(x)V(x)V(x) and scattering from a finite set of $\ensuremath{\delta}$-function potentials of arbitrary positions and strengths is found.
The Schrödinger equation for a particle in the V-shaped potential decorated by a repulsive or attractive Dirac delta function interaction at the center is solved, demonstrating the crucial influence of point interaction on the even-parity states of the original system without decoration. As strength of the attraction increases, the ground state energy falls down without limit; and in limit of infinitely large attraction, the ground state approaches a singular state. Our analysis and conclusion can be readily generalized to any one-dimensional system a particle interacts with symmetrical potential plus the Dirac delta function interaction at the center.