| Summary: | 碩士 === 國立交通大學 === 應用數學系所 === 92 === There are two parts in the thesis. In the first part, we discuss the discretization in the quantum well, wire, and dot. For the interface condition, we use different discretizations to the model equation, and compare the results. Because the interface condition is very important, we use different discretizations to the interface condition and get different convergent results about the smallest eigenvalue. In the second part, we use some substitutions
to reduce the dimension on the matrix A in the eigenvalue system Ax=λx, and get the smallest eigenvalue which
is very close to the one of the original matrix A. Since the
wave function can be very smooth, there is no need in solving the whole system with very fine mesh. Therefore, we use some substitutions to reduce the dimension of the matrix A and we can still get very accurate eigenvalue.
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