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œ otherwise

The corresponding Schrodinger equation can be written as

where e is the total energy and the wavefunction y) must satisfy the boundary condition fi(x, ±y,) = 0

As has been pointed out by Jan and Lee [151], as the strip becomes very narrow (i.e., y0 is very small), the fast motion in the y-direction allows the wavefunction to be written, approximately, as fi(x, y) « x(y)®(x)

Since y) must satisfy the boundary condition (276), then

Introducing Eq. (277) into Eq. (275) and multiplying the result by cos(k0y), the integration over y from —y0 to y0 yields the equation dL

where

is a normalization constant and ey = k2 = n2 /4y2 is the kinetic energy of the fast motion in the y-direction due to confinement.

Equation (279) can be rewritten as d2

0 0

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