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Multiple choice
At a boundary
x
=
a
x = a
x
=
a
where the potential
V
V
V
is FINITE, which boundary conditions must the wavefunction
ψ
\psi
ψ
satisfy when matching the solutions
ψ
L
\psi_L
ψ
L
(left) and
ψ
R
\psi_R
ψ
R
(right)?
Both
ψ
\psi
ψ
and its first derivative
d
ψ
/
d
x
d\psi/dx
d
ψ
/
d
x
are continuous:
ψ
L
(
a
)
=
ψ
R
(
a
)
\psi_L(a) = \psi_R(a)
ψ
L
(
a
)
=
ψ
R
(
a
)
and
ψ
L
′
(
a
)
=
ψ
R
′
(
a
)
\psi_L'(a) = \psi_R'(a)
ψ
L
′
(
a
)
=
ψ
R
′
(
a
)
Only the derivative
d
ψ
/
d
x
d\psi/dx
d
ψ
/
d
x
must be continuous;
ψ
\psi
ψ
itself may be discontinuous
ψ
\psi
ψ
must equal zero at the boundary, just as at an infinite wall
Only
ψ
\psi
ψ
must be continuous; its derivative
d
ψ
/
d
x
d\psi/dx
d
ψ
/
d
x
may jump arbitrarily for any finite
V
V
V
Check answer