### Abstract

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

Pages (from-to) | 469-481 |

Number of pages | 420 |

Journal | International Journal of Theoretical Physics |

DOIs | |

State | Published - 1 Jan 2000 |

Externally published | Yes |

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**Levinson's theorem for the Schrödinger equation in one dimension.** / Dong, Shi Hai; Ma, Zhong Qi.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Levinson's theorem for the Schrödinger equation in one dimension

AU - Dong, Shi Hai

AU - Ma, Zhong Qi

PY - 2000/1/1

Y1 - 2000/1/1

N2 - Levinson's theorem for the one-dimensional Schrödinger equation with a symmetric potential which decays at infinity faster than x-2 is established by the Sturm-Liouville theorem. The critical case where the Schrödinger equation has a finite zero-energy solution is also analyzed. It is demonstrated that the number of bound states with even (odd) parity n+(n-) is related to the phase shift η+(0) [η-(0)] of the scattering states with the same parity at zero momentum as η+(0) + π/2 = n+π and η-(0) = n-π for the noncritical case, and η+(0) = n+π and η-(0) - π/2 = n-π for the critical case.

AB - Levinson's theorem for the one-dimensional Schrödinger equation with a symmetric potential which decays at infinity faster than x-2 is established by the Sturm-Liouville theorem. The critical case where the Schrödinger equation has a finite zero-energy solution is also analyzed. It is demonstrated that the number of bound states with even (odd) parity n+(n-) is related to the phase shift η+(0) [η-(0)] of the scattering states with the same parity at zero momentum as η+(0) + π/2 = n+π and η-(0) = n-π for the noncritical case, and η+(0) = n+π and η-(0) - π/2 = n-π for the critical case.

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=0034134760&origin=inward

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U2 - 10.1023/A:1003604830131

DO - 10.1023/A:1003604830131

M3 - Article

SP - 469

EP - 481

JO - International Journal of Theoretical Physics

JF - International Journal of Theoretical Physics

SN - 0020-7748

ER -