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Since the electron energy w i t h i n the barrier region suffers a time-dependent p e r t u r b a t i o n , the perturbed electronic wavefunction at any instant may be expressed as a linear combination of the unperturbed wavefunctions ( 1 1 5 ) . 46) where a(t) and bit) are the time-dependent constants. tyo(x) exp{- [ftiJA]t} and ψ ix) exp{- \_(iE ) /ft]t] are the solu­ tions of the unperturbed tiffie-dependent §chrodingerfs equation, viz. 49) where a and 3 are constants to be determined by matching iK and ψ Γ along with their derivatives at x=o and at x=w, with the incident and transmitted waves, respectively.

I /cj_ , -,, 2 η ΛΔ ^ 1 where j and j. represent the transmitted and incident current älnsities respectively. >««·♦ »o · <'- ' It should, h o w e v e r , be remembered that Z(w) measures the tunnel­ ling probability of electrons appearing at the same energy since the problem has been considered time-independent at the first instance. Since the electron energy w i t h i n the barrier region suffers a time-dependent p e r t u r b a t i o n , the perturbed electronic wavefunction at any instant may be expressed as a linear combination of the unperturbed wavefunctions ( 1 1 5 ) .

J. P. Wilson, Phys. Letts. 28A (1968) 43. 34 Tunnelling and Negative Resistance Phenomena (76) N. V. Zavaritskii, Proceedings of the 8th International Conference on Low Temperature Physics (R. 0. 175 (1963); JETP 18 (1964) 1260; JETP 2\_ (1965) 557. (77) J. P. Franck and W. J. Keeler, Phys. Rev. Lett. 20 (1968) — 379. F. Reif and M. A. Wolf, Phys. Rev. Lett. £ (1962) 315. S. M. Marcus, Phys. Letts. _2_3 (1966) 28. T. D. Clark, Phys. Letts. _24A (1967) 459. J. Klein and A. Leger, Phys. Letts. 30A (1969) 96.

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