Effective Generating Functions for Quantum Canonical Transformations

Aug 8, 1986
24 pages
Published in:
  • Phys.Rev.D 35 (1987) 1289
Report number:
  • UFTP-86-15

Citations per year

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Abstract: (APS)
An effective generating function F(q,Q) is introduced for any given pair of quantum-mechanical systems whose classical Hamiltonians are canonically equivalent. Using eiF as a kernel, an integral transform relates the wave functions of the corresponding quantum systems. The function F reduces in the classical limit (ħ→0) to the generating function of the classical transformation. Conversely, starting with the classical form, F can be calculated in a recurrent fashion, order by order in powers of ħ. For the canonical transformation that relates a particle moving in an exponential (Liouville) potential to a free particle, the effective quantum generating function is identical to its classical counterpart. The generalization to quantum field theory is possible using the Schrödinger wave-functional formalism.
  • QUANTUM MECHANICS: WAVE FUNCTION
  • TRANSFORMATION: CANONICAL
  • TRANSFORMATION: BAECKLUND
  • FIELD EQUATIONS: LIOUVILLE
  • PROPAGATOR