13．. (x) and 2(x) are both non-trivial solutions (i.e., ψ1,2 are not zero everywhere) of the timeindependent 1D Schrodinger equation. Which of the following is not a solution to that Schrodingerequation? (Note: A, B, and a are arbitrary, non-zero constants. This question only asks for 'mathematical solution' to the Schrodinger equation. You don't need to normalize the wave functionsnor fulfill any boundary conditions.)(A)Aψ₁(x) (B)Aψ₁(x)+Bψ₂(x) (C)(A+B)·(ψ₁(x)+ψ₂(x)) (D)ψ₁(x)·eα + ψ₂(x)·e-α (E)None of the above is a solution.

1. For a particle with an energy of E tunneling through a finite barrier height of U and width of & solve the Schrodinger wave equation to calculate the tunneling probability and select the correct answer corresponding to various E, U, and 8 for different particles. (A) For a neutron with E = 50 meV incident on a barrier of U = 250 meV and 8 = 0.16 nm, the tunneling probability is 4.45×10-11 = 0.0445 ppb (B) For a neutron with E = 50 meV incident on a barrier of U = 250 meV and 8 = 0.1 nm, the tunneling probability is 5.86×10-10 = 0.586 ppb (C) For an electron with E = 1.0 eV incident on a barrier with U = 5.0 eV and 8 = 0.5 nm, the tunneling probability is 7.1×10-7 = 0.71 ppm (D) For an electron with E = 1.0 eV incident on a barrier with U = 5.0 eV and 8 = 1.0 nm, the tunneling probability is 2.52×10-9 =2.52 ppb (E) For an electron with E = 1.0 eV incident on a barrier with U = 5.0 eV and & = 1.25 nm, the tunneling probability is 1.5×10-10 = 0.15 ppb

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