Xq gqnPoqa

where fi0(q' a) has a structure similar to the solution of the Schrodinger equation for H0, but the good quantum num-ber(s) that define the energy of the free system is (are) replaced by a parameter (or a set of parameters) a, because the confining conditions impose new quantization rules.

The function g(q) must satisfy the boundary condition given by Eq. (98). This technique can be used when the symmetry of the confining potential is compatible with the symmetry of the system under study.

When the latter is not the case, the form of the trial wave-function given by Eq. (99) must be slightly changed since the symmetry is broken by the confinement potential. However, in spite of the lack of compatibility between both symmetries, the system and confinement domain often are related through a coordinate transformation of the form q = q(q)

where q' are the coordinates of the center of symmetry of D and q are the coordinates of the center of symmetry of the system.

Even in the aforementioned case, it is still possible to construct the trial wavefunction as in Eq. (99), except that the coordinates q of the system under study must be written in terms of the coordinates q' of D using the rule given in Eq. (100). Under such conditions the trial wavefunction for this asymmetry situation can be written as x(q(q')) = g(q(q'))no(q(q'),a)

Once the latter has been done, the energy functional can be constructed and minimized with respect to a, as usual.

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