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Physica A Statistical Mechanics and its Applications

Feynman propagator and space-time transformation technique

Antonio Boulhosa Nassar

Published Feb 1, 1987• 12 citations
Publisher
DOI
10.1016/0378-4371(87)90259-7

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A calculation for the Kanai–Caldirola propagator in the de Broglie–Bohm theory is proposed. The technique of space-time transformations used in the Feynman path integral is adapted and then the problem is converted to that of the harmonic oscillator. The quantum propagator is viewed as an expansion of the guiding wave function over the velocity space. The construction is re-examined by replacing the integration over the initial velocity of the classic path by its final extremity. This gives a certain affinity with the Feynman path integral approach.
The bound state solutions of the Feynman propagator with the rotating Deng- Fan molecular potential are presented approximately. An approximation of the centrifugal potential is used and nonlinear space-time transformations are applied. A relation between the original path integral and the Green function of a new quantum soluble system is derived. The energy spectrum and the normalized eigenfunctions are both obtained for the application of this technique to the Deng-Fan molecular potential. Our results are in very good agreement with those found by using numerical and other methods.