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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 PhysicsJul 1, 199416 citations

Quantum unbinding in potentials with 1/r P tails

Royce K. P. Zia, Reinhard Lipowsky, D. M. Kroll

Potentials with repulsive power behavior at large distances may or may not have a zero-energy bound state, depending only on the power p and, if p=2, the strength. For the case of no zero-energy bound state, we further study how the state unbinds as the attractive, small r part of the potential is tuned to let the binding energy go to zero. Although motivated by the physics of wetting, this problem is well suited for senior or graduate level quantum mechanics courses by giving a novel perspective of solutions to one-dimensional Schroedinger equations.Potentials with repulsive power behavior at large distances may or may not have a zero-energy bound state, depending only on the power p and, if p=2, the strength. For the case of no zero-energy bound state, we further study how the state unbinds as the attractive, small r part of the potential is tuned to let the binding energy go to zero. Although motivated by the physics of wetting, this problem is well suited for senior or graduate level quantum mechanics courses by giving a novel perspective of solutions to one-dimensional Schroedinger equations.

American Journal of PhysicsFeb 1, 198824 citations

Quantum anticentrifugal force

M. A. Cirone, Kazimierz Rza̧żewski, Wolfgang P. Schleich +2 more

In a two-dimensional world, a free quantum particle of vanishing angular momentum experiences an attractive force. This force originates from a modification of the classical centrifugal force due to the wave nature of the particle. For positive energies the quantum anticentrifugal force manifests itself in a bunching of the nodes of the energy wave functions towards the origin. For negative energies this force is sufficient to create a bound state in a two-dimensional \ensuremath{\delta}-function potential. In a counterintuitive way, the attractive force pushes the particle away from the location of the \ensuremath{\delta}-function potential. As a consequence, the particle is localized in a band-shaped domain around the origin.In a two-dimensional world, a free quantum particle of vanishing angular momentum experiences an attractive force. This force originates from a modification of the classical centrifugal force due to the wave nature of the particle. For positive energies the quantum anticentrifugal force manifests itself in a bunching of the nodes of the energy wave functions towards the origin. For negative energies this force is sufficient to create a bound state in a two-dimensional \ensuremath{\delta}-function potential. In a counterintuitive way, the attractive force pushes the particle away from the location of the \ensuremath{\delta}-function potential. As a consequence, the particle is localized in a band-shaped domain around the origin.

arXiv:quant-ph/0108069Physical Review ADec 21, 200139 citations

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

Haydar Uncu, Ersan Demiralp

Physics Letters AJun 23, 200616 citations

Modified Dirac delta function and modified dirac delta potential in the quantum mechanics

Won Sang Chung, HASSAN HASSANABADI

The European Physical Journal PlusJan 1, 20222 citations

Quantum solutions for the delta ring and delta shell

Luis F. Castillo-Sánchez, Julio C. Gutiérrez-Vega

The quantum description of a free particle subject to a delta circular ring and a delta spherical shell is studied. We determine the bound eigenstates and energy spectra for different angular momentum states. The normalization constants of the bound states and the transmission and reflection coefficients of the scattering states are calculated in closed form. The ground state of the delta ring is always present regardless of the potential strength. In contrast, the delta shell requires a threshold of the delta strength for the first eigenstate to appear. For the ring and the shell, the wave functions tend to be degenerate at high energies, and the effect of angular momentum on the wave functions becomes negligible. This work generalizes the standard problem of the one-dimensional delta potential studied in textbooks.The quantum description of a free particle subject to a delta circular ring and a delta spherical shell is studied. We determine the bound eigenstates and energy spectra for different angular momentum states. The normalization constants of the bound states and the transmission and reflection coefficients of the scattering states are calculated in closed form. The ground state of the delta ring is always present regardless of the potential strength. In contrast, the delta shell requires a threshold of the delta strength for the first eigenstate to appear. For the ring and the shell, the wave functions tend to be degenerate at high energies, and the effect of angular momentum on the wave functions becomes negligible. This work generalizes the standard problem of the one-dimensional delta potential studied in textbooks.

American Journal of PhysicsJun 20, 20252 citations

A Quantum Physics Jeopardy Problem of a One-Bound-State Double Dirac Delta Potential with a Centrifugal, Angular-Momentum-Like Tail

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A Quantum Physics Jeopardy Problem of a One-Bound-State Double Dirac Delta Potential with a Centrifugal, Angular-Momentum-Like Tail

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