Quantum bound states with zero binding energy

Jamil Daboul, Michael Martin Nieto

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


After reviewing the general properties of zero-energy quantum states, we give the explicit solutions of the Schrödinger equation with E = 0 for the class of potentials V = -|γ|/rν, where -∞ < ν < ∞. For ν > 2, these solutions are normalizable and correspond to bound states, if the angular momentum quantum number l > 0. (These states are normalizable, even for l = 0, if we increase the space dimension, D, beyond 4; i.e for D > 4.) For ν < -2 the above solutions, although unbound, are normalizable. This is true even though the corresponding potentials are repulsive for all r. We discuss the physics of these unusual effects.

Original languageEnglish
Pages (from-to)357-362
Number of pages6
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Issue number5-6
StatePublished - 1 Aug 1994

ASJC Scopus subject areas

  • Physics and Astronomy (all)


Dive into the research topics of 'Quantum bound states with zero binding energy'. Together they form a unique fingerprint.

Cite this