One-dimensional tunnel-junction formula for the schrödinger particle

Masao Hirokawa, Takuya Kosaka

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We handle all the self-adjoint extensions of the minimal Schrödinger operator for the nonrelativistic electron living in the one-dimensional configuration space with a junction. We are interested in every boundary condition corresponding to the individual self-adjoint extension. Thus, we clarify all the types of those boundary conditions of the wave functions of the nonrelativistic electron. We find concrete tunnel-junction formulae for the nonrelativistic electron passing through the junction, which reveals the phase factor caused by the tunneling through the junction. Using this tunnel-junction formula, we propose a mathematical possibility of a tunnel-junction device for qubit.

Original languageEnglish
Pages (from-to)2247-2261
Number of pages15
JournalSIAM Journal on Applied Mathematics
Issue number6
Publication statusPublished - 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Applied Mathematics


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