[ Please Note: When we match the different wavefunctions and their first derivat

Question

[Please Note: When we match the different wavefunctions and their first derivatives, we are matching them only at the interface or boundary between them, not for all x. The latter would never make sense - they would all have to be zero (or constant) all the time.] Remember that the first and second wavefunctions match only at x = 0 and the second and third match only at x = L. I added a, b, and c subscripts to help you think this through.   Ya = Yb only at x = 0 and Yb = Yc only at x = L, and the same for the first derivatives.

Problem:

The total wave function for a particle in 3 regions is given by

Ya(x) = A e^-ax x < 0

Yb(x) = B coskx 0 < x < L

Explanation / Answer

Boundary Condition :

Ya(0) = Yb(0) ; Yb(L) = Yc(L)

==> A = B ; BcoskL = Ce^(-k0L)

& Yb'(L) = Yc'(L)

==> -BksinkL = -Ck0e^(-koL)

==> ktankL = K0

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.