Question

1. An electron in a finite well An electron is in a finite square well that is 20 eV deep and 0.25 nm wide. You may use all results from class/textbook without re-deriving therm A. (2 pts) By graphing both sides of the quantization condition like we did in class, determine how many bound energy eigenstates exist for this well. Don't forget that there are two quantization conditions, one for the even solutions, and one for the odd solutions! B. (6 pts) Solve numerically for the energy of the ground state AND the highest energy bound state of this system to within 2 significant digits. You may do this any way you want (guess and check (4 pts) Define the "penetration depth" (relevant for the classically forbidden regions) to be 6- , and the "wavelength" (relevant for the classically allowed region) to be . Compute δ and λ for the ground state and the highest energy bound with a spreadsheet, other software...), but describe how you did it for full credit. C 1/q 2m(Vo - E) 2πν2mE state. Use these values to make a sketch of these two wave functions.

Answer 1

2.J 2 0 B) Vo- 20e. 2n- )- 5 그n-1 3.26 7 2

2.J 2 0 B) Vo- 20e. 2n- )- 5 그n-1 3.26 7 2