Nonlinear Spectrum and Generating Algebra for Infinitely Deep Square Well Potential and New Coherent State

NI Zhi-Xiang

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《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 2001, Vol. 25> Issue(6) : 487-493

Nonlinear Spectrum and Generating Algebra for Infinitely Deep Square Well Potential and New Coherent State

NI Zhi-Xiang ^,

Department of Physics,Fuyang Teachers College,Fuyang 236032, ChinaDepartment of Physics,Xuzhou Normal University,Xuzhou 221009,China

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Abstract：
Using the Hamiltonian of symmetrical one dimersional infinitely deep square well potential and natural operators,we obtain its nonlinear spectrum and generating algebra,and get a class of new nonlinear coherent states on the basis of the nonlinear algebra obfained. These coherent states are of temporal stability,and can be regarded as the eigenstates of the lower operator with the eigenvalues in an operator field and as the rotational states of the generalized minimal uncertainly states as well.

References

[1]

. Bender C M ,Boettcher S ,Jones H F et al.J.Phys.,1999,A3 2 :6771 2. NI Zhi-Xiang .High Energy Physics and Nuclear Physics,1999,23 :289(in Chinese)(倪致祥.高能物理与核物理,1999,23:289)3. Beckers J,Brihaye Y ,Debergh N . J.Phys.,1999,A3 2 :27914. NI Zhi-Xiang .Phys.Lett.,1997,A2 3 5:313 5. CHEN Jing-Ling ,LIU Yong,GE Mo-Lin .J .Phys.,1998,A31 :6473 6. Quesne C .J.Phys.,1999,A2 :6705 7. NI Zhi-Xiang .ActaPhysicaSinica,1999,8:8 8. NietoMM ,Jr Simmons L M .Phys.Rev.,1979,D20:1321 9. Perelomow A .Generalized Coherent States and Their Applications.Springer-Verlag ,Berlin:1986 10. Junke rG ,ROY P .Phys.Lett.,1999,A257:11311. Klauder J R.J.Phys.,1996,A29:L29312. HAN Qi-Zhi,SUN Hong-Zhou.Group Theory.Beijing University,1987,225(in Chinese)(韩其智,孙洪洲.群论.北京大学出版社,1987.225) 13. WANG Zhu-Xi,GUO Dun-Ren.An Introduction to Special Functions,Beijing:Science Press,1979.412 (in Chinese)(王竹溪. 郭敦仁.特殊函数概论,北京:科学出版社,1979.412) 14. NI Zhi-Xiang.Acta Physica Sinica,1998,7:183

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NI Zhi-Xiang. Nonlinear Spectrum and Generating Algebra for Infinitely Deep Square Well Potential and New Coherent State[J]. Chinese Physics C, 2001, 25(6): 487-493.

NI Zhi-Xiang. Nonlinear Spectrum and Generating Algebra for Infinitely Deep Square Well Potential and New Coherent State[J]. Chinese Physics C, 2001, 25(6): 487-493. shu

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Received: 2000-06-15
Revised: 1900-01-01

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沈阳化工大学材料科学与工程学院沈阳 110142

Nonlinear Spectrum and Generating Algebra for Infinitely Deep Square Well Potential and New Coherent State

NI Zhi-Xiang ^,

Corresponding author: NI Zhi-Xiang,

Department of Physics,Fuyang Teachers College,Fuyang 236032, ChinaDepartment of Physics,Xuzhou Normal University,Xuzhou 221009,China

Received Date: 2000-06-15
Accepted Date: 1900-01-01
Available Online: 2001-06-05

Abstract: Using the Hamiltonian of symmetrical one dimersional infinitely deep square well potential and natural operators,we obtain its nonlinear spectrum and generating algebra,and get a class of new nonlinear coherent states on the basis of the nonlinear algebra obfained. These coherent states are of temporal stability,and can be regarded as the eigenstates of the lower operator with the eigenvalues in an operator field and as the rotational states of the generalized minimal uncertainly states as well.