Probabilistic interpretation of resonant states

Pramana

Joshua Feinberg3³  Naomichi Hatano1²  Tatsuro Kawamoto¹ 

[1]Department of Physics, University of Tokyo, Komaba, Meguro, Tokyo 153-8505, Japan$$

[2]Institute of Industrial Science, University of Tokyo, Komaba, Meguro, Tokyo 153-8505, Japan$$

[3]Department of Physics, University of Haifa at Oranim, Qiryat Tivon 36006, Israel$$

关键词: Resonance;    probabilistic interpretation;    normalization.;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

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.

【 授权许可】

Unknown