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The hydrogen atom in one dimension

 

作者: R. E. Moss,  

 

期刊: American Journal of Physics  （AIP Available online 1987）
卷期: Volume 55, issue 5  

页码: 397-401

 

ISSN:0002-9505

 

年代: 1987

 

DOI:10.1119/1.15144

 

出版商: American Association of Physics Teachers

 

关键词: DIRAC EQUATION;SCHROEDINGER EQUATION;KLEIN−GORDON EQUATION;BINDING ENERGY;HYDROGEN;ATOMS;BOUND STATE;ONE−DIMENSIONAL CALCULATIONS;GROUND STATES

 

数据来源: AIP

 

摘要:

The Schrödinger, Klein–Gordon, and Dirac equations for the hydrogen atom are solved inDdimensions, whereDmay be noninteger. ForD=1 the nondegenerate ground state with infinite binding energy is obtained as a limit asDtends to 1 for the Schrödinger equation. The corresponding solution of the Klein–Gordon equation is shown to be unacceptable, contradicting previous work. Unexpectedly, no bound state solutions of the Dirac equation withD=1 are found at all. A few comments are made on theD=3 and 2 cases.

 

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