Research Article
Wide Effectiveness of a Sine Basis for Quantum-Mechanical Problems in Dimensions
Table 4
Approximation of the energy levels of the harmonic oscillator in dimensions . represents the energy state, is the exact solution for the energy given by (12), and is the upper bound to obtained using the variational analysis. The eigenvalues of H are minimized over . This table shows specific examples of energy values for the quantum numbers and energy states . Note that the approximation error has diminished compared with those of Table 3. In the worst case it is of , while in others cases the upper bounds are almost exact.
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