PHY4604 R. D. Field Department of Physics Chapter2_27.doc University of Florida Quantum Mechanical Tunneling (2) Boundary Conditions:There are four boundary conditions. At x = 0we have )0()0(21ψψ=which implies DCBA+=+0201===xxdxddxdψψwhich implies DCikBikAκκ−=−and at x = Lwe have )()(32LLψψ=which implies ikLLLFeDeCe+−+=+κκLxLxdxddxd===32ψψwhich implies ikLLLikFeDeCe+−+=−κκκκWe now must solve for B, C, D, and Fin terms of A. We have four equations and four unknowns: 000000111=−−+=−++−=++−−−=+−−++−++−+FikeDeCeBFeDeCeBikAFDCikBAFDCBikLLLikLLLκκκκκκκκI will use determinates to solve these simultaneous linear equations as follows: ()()()()())cosh(2)sinh()(2)(2))(()()()()()()(101110110000111222222LikLkeeeikeekeikeikeeikeikeikeikeikeeikeeeeikeike
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