We now consider the system as confined within a prolate spheroidal box of eccentricity 1/g0 and barrier height V0. The corresponding modified Hamiltonian is then


The formal solutions of the Schrodinger equation for the inner (£ < £0) and outer (£ > £0) regions must satisfy continuity conditions at the boundary (£ = £0), which are equivalent to

Equation (223) allows us to find the energy of the system if an explicit form of the wavefunction is known.

The V0 = x case was studied exactly by Ley-Koo and Cruz [120]. An approximate study of these systems for finite values of V0 can be performed using a direct variational method. In this case an ansatz wavefunction x must be constructed. Following Refs. [78, 121], we have and

where ^0 and ^0 are the solutions of the Schrodinger equation for the free system [122, 123], f is an auxiliary function which allows the total wavefunction to satisfy the condition shown in Eq. (223), and a is a variational parameter i'=0

to be determined once the corresponding energy functional is minimized with the additional constrictions improved by Eq. (223).

Following Coulson [122], the ansatz wavefunction for the ground state is constructed as

0 0

Post a comment