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    • Keywords


      Resonance; probabilistic interpretation; normalization.

    • Abstract


      We provide probabilistic interpretation of resonant states. We do this by showing that the integral of the modulus square of resonance wave functions (i.e., the conventional norm) over a properly expanding spatial domain is independent of time, and therefore leads to probability conservation. This is in contrast with the conventional employment of a bi-orthogonal basis that precludes probabilistic interpretation, since wave functions of resonant states diverge exponentially in space. On the other hand, resonant states decay exponentially in time, because momentum leaks out of the central scattering area. This momentum leakage is also the reason for the spatial exponential divergence of resonant state. It is by combining the opposite temporal and spatial behaviours of resonant states that we arrive at our probabilistic interpretation of these states. The physical need to normalize resonant wave functions over an expanding spatial domain arises because particles leak out of the region which contains the potential range and escape to infinity, and one has to include them in the total count of particles.

    • Author Affiliations


      Naomichi Hatano1 Tatsuro Kawamoto2 Joshua Feinberg3 4

      1. Institute of Industrial Science, University of Tokyo, Komaba, Meguro, Tokyo 153-8505, Japan
      2. Department of Physics, University of Tokyo, Komaba, Meguro, Tokyo 153-8505, Japan
      3. Department of Physics, University of Haifa at Oranim, Qiryat Tivon 36006, Israel
      4. Department of Physics, Technion, Haifa 32000, Israel
    • Dates

  • Pramana – Journal of Physics | News

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