Communications in Theoretical Physics

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Quantum Mechanical Version of z-Transform Related to Eigenkets of Boson Creation Operator


FAN Hong-Yi,1,2 FU Liang,3 and A. Wunsche4   


  1. 1 Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, China
    2 Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China
    3 Special Class for the Gifted Young, University of Science and Technology of China, Hefei 230026, China
    4 Institut fur Physik, Humboldt-Universitat, Invalidenstr. 110, 10115 Berlin, Germany
  • Received: 2003-10-22 Revised: 1900-01-01 Published: 2004-11-15

Abstract: Using the completeness relation composed of the coherent state and of the eigenket of bosonic creation operator, we establish a one-to-one correspondence between the z-transform and the quantum-mechanical transform from the representation by number states |n> to the representation by coherent states |(z)> (Bargmann representation). In this way, the quantum-mechanical version of the various properties of z-transform are obtained and the operators for embodying these properties in the Fock space are derived, which may find applications in quantum states engineering.

Key words: z-transform, eigenket of creation operator, coherent state

PACS numbers: 

  • 03.65.Ca