Chinese Journal of Quantum Electronics, Volume. 28, Issue 5, 534(2011)
Reflection and transmission of material wave through an arbitrary potential barrier
Based on the similarity between time-independent Schr?dinger equation and Helmholtz equation, the analytical transfer matrix method was utilized to analyze macroscopic quantum tunneling effect, and the potential filed and eigenvalue were corresponded to the refractive index and propagation constant, respectively. Without solving the Schr?dinger equation and any approximation, the exact analytic expressions of reflection coefficient and reflection probability of the particle were obtained. Initial results show the equations obtained here are exact and have clear physical meanings. It is expected to be applied in the researches of many basic quantum phenomena, such as quantum tunneling effect, quantum reflection, quantum particles and tunneling resonance.
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XIAO Ping-ping, DENG Man-lan. Reflection and transmission of material wave through an arbitrary potential barrier[J]. Chinese Journal of Quantum Electronics, 2011, 28(5): 534
Received: Nov. 11, 2010
Accepted: --
Published Online: Sep. 27, 2011
The Author Email: Ping-ping XIAO (xpp7967@163.com)