Figure 2 - uploaded by Teemu Isojärvi
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Potential energy function V (x) (left) and the positions of rst 5 eigenvalues (right) for the approximate 4-level system, a 1-dimensional QPW of length L = 2, depth V 0 = 600 and perturbed with additional potential energy term (17).
Source publication
In this article, a method is described for modifying a 1D square potential well in a way that converts it to an effective n-level system with a large energy gap between the n:th eigenvalue of the Hamiltonian and the higher eigenvalues, with n varying from 2 to 5. The method is based on forming potential energy perturbation terms that have a large o...
Contexts in source publication
Context 1
... A 2 = 14.0, A 3 = 8.6, A 4 = −38.2 and A 5 = 20.5 produced a spectrum with spacings E 2 − E 1 , E 3 − E 2 and E 4 − E 3 being close to their average and an energy gap of E 5 − E 4 > 3.5(E 4 − E 1 ) above the rst four eigenvalues. A graph of the combined potential energy V (x) + V (x) and the locations of rst ve energy eigenvalues are shown in Fig. 2. The eigenenergies for the potential wells with parameters listed in Table 2 were calculated with the C++ code that nds rst 5 eigenvalues with the shooting method. The results are listed, with the quotients R 2 and R 3 , in Table 5. Table 5: The rst ve eigenenergies E n with a perturbation term being of ...
Context 2
... rst probability densities |ψ (1) k (x)| 2 , made to drop to zero after |x| = 1.05L/2 and normalized to 1, after the rst round are shown in Fig. 8. 5 | is signicantly larger than all of them combined. The amount of diculty experienced in nding the right coecients C (l) k for this modication was similar to that in forming the 4-level system of Fig. 2 in a one-step process, and seemed to imply that 3 modication steps would be more appropriate for this number of spectral lines. The number of maxima and minima in the potential energy functions like those shown in Figs. 6 and 9 increases when more low-energy states are separated from the rest of the spectrum with an energy gap. An ...
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