### Abstract

Original language | American English |
---|---|

Pages (from-to) | 2790-2796 |

Number of pages | 2510 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

DOIs | |

State | Published - 1 Jan 1998 |

Externally published | Yes |

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### Cite this

*Physical Review A - Atomic, Molecular, and Optical Physics*, 2790-2796. https://doi.org/10.1103/PhysRevA.58.2790

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*Physical Review A - Atomic, Molecular, and Optical Physics*, pp. 2790-2796. https://doi.org/10.1103/PhysRevA.58.2790

**Levinson’s theorem for the Schrödinger equation in two dimensions.** / Dong, Shi Hai; Hou, Xi Wen; Ma, Zhong Qi.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Levinson’s theorem for the Schrödinger equation in two dimensions

AU - Dong, Shi Hai

AU - Hou, Xi Wen

AU - Ma, Zhong Qi

PY - 1998/1/1

Y1 - 1998/1/1

N2 - Levinson’s theorem for the Schrödinger equation with a cylindrically symmetric potential in two dimensions is reestablished by the Sturm-Liouville theorem. The critical case, where the Schrödinger equation has a finite zero-energy solution, is analyzed in detail. It is shown that, in comparison to Levinson’s theorem in the noncritical case, the half bound state for the [Formula Presented] wave, in which the wave function for the zero-energy solution does not decay fast enough at infinity to be square integrable, will cause the phase shift of the [Formula Presented] wave at zero energy to increase an additional [Formula Presented]. © 1998 The American Physical Society.

AB - Levinson’s theorem for the Schrödinger equation with a cylindrically symmetric potential in two dimensions is reestablished by the Sturm-Liouville theorem. The critical case, where the Schrödinger equation has a finite zero-energy solution, is analyzed in detail. It is shown that, in comparison to Levinson’s theorem in the noncritical case, the half bound state for the [Formula Presented] wave, in which the wave function for the zero-energy solution does not decay fast enough at infinity to be square integrable, will cause the phase shift of the [Formula Presented] wave at zero energy to increase an additional [Formula Presented]. © 1998 The American Physical Society.

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=0001562091&origin=inward

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U2 - 10.1103/PhysRevA.58.2790

DO - 10.1103/PhysRevA.58.2790

M3 - Article

SP - 2790

EP - 2796

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

ER -