Quantum Mechanics and Electrodynamics by Jaroslav Zamastil & Jakub Benda

Author:Jaroslav Zamastil & Jakub Benda
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(6.128)

For an electron leaving the atom along the positive direction of the z-axis, i.e., for z → ∞, we easily find that r → ∞ and consequently ξ → ∞. On the other hand, the coordinate η could still be finite in this limit, see Fig. 6.2. Therefore, shall Eq. (6.128) hold, we need to search for a solution to Eq. (6.127) of the form

Fig. 6.2Parabolic coordinates. The dashed lines are the lines of constant ξ, the continuous ones of constant η

(6.129)

By inserting Eq. (6.129) into Eq. (6.127), we obtain an equation for the function ϕ(ξ), namely

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