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Multiple choice
For the infinite square well with walls at
x
=
0
x=0
x
=
0
and
x
=
L
x=L
x
=
L
, the general solution inside is
ψ
(
x
)
=
A
sin
(
k
x
)
+
B
cos
(
k
x
)
\psi(x) = A\sin(kx) + B\cos(kx)
ψ
(
x
)
=
A
sin
(
k
x
)
+
B
cos
(
k
x
)
. After applying the boundary conditions
ψ
(
0
)
=
0
\psi(0)=0
ψ
(
0
)
=
0
and
ψ
(
L
)
=
0
\psi(L)=0
ψ
(
L
)
=
0
, what results?
🔬 try it before you answer
A
=
0
A = 0
A
=
0
, and
k
k
k
can take any positive real value
Both
A
A
A
and
B
B
B
are nonzero, and
k
=
π
/
(
2
L
)
k = \pi/(2L)
k
=
π
/
(
2
L
)
is the only solution
B
=
0
B = 0
B
=
0
, and
k
k
k
is unrestricted (any real
k
k
k
is allowed)
B
=
0
B = 0
B
=
0
, and
k
k
k
is restricted to
k
n
=
n
π
/
L
k_n = n\pi/L
k
n
=
nπ
/
L
for positive integers
n
n
n
Check answer