Use of Psi Squared and Flux to Simplify Analysis of Transmission past Rectangular Barriers or Wells.

Htay Yee, Thida Win Aye Aye Myint Kyaw Kyaw Naing, Aye Than Kyae

S. Bose, J. Mitra, P. Mandal

James E. Draper

The transmission coefficient for a completely general one-dimensional rectangular potential barrier or well, or series of steps, is analyzed simply by concentrating on ‖Ψ‖2 rather than Ψ. Graphs of ‖Ψ‖2 for all cases are given, whereas only two textbooks graph anything related to Ψ, and those plots of Re(Ψ) can be misinterpreted.

Mário Goto, H. Iwamoto, Verissimo Manoel de Aquino +1 more

James E. Draper

The transmission coefficient for quantal tunneling through a rectangular, one-dimensional potential barrier is analyzed. By employing continuity of ‖ ψ ‖2 and flux the results, even with an asymmetrical barrier, are obtained easily. The asymmetrical barrier has the same transmission in either direction. Considerable insight into the form of the most physical quantity, ‖ ψ(x) ‖2, is afforded with little algebra. Graphs of transmission are given for general barriers, and properties of the solutions are discussed.

Angelo Tartaglia, E. Ferraris, E. Gonnelli