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QM · Ch 1 · Gaussian wave packet normalization and ⟨x²⟩
Physics · Quantum Mechanics · Griffiths Ch 1
Problem
A particle's wave function at
t
=
0
t=0
t
=
0
is
ψ
(
x
,
0
)
=
A
e
−
λ
x
2
\psi(x,0) = A\,e^{-\lambda x^2}
ψ
(
x
,
0
)
=
A
e
−
λ
x
2
with
λ
>
0
\lambda > 0
λ
>
0
real. (a) Find
A
A
A
from normalization. (b) Compute
⟨
x
⟩
\langle x \rangle
⟨
x
⟩
,
⟨
x
2
⟩
\langle x^2 \rangle
⟨
x
2
⟩
, and the position uncertainty
σ
x
\sigma_x
σ
x
.
Related theory
Symmetries In Quantum Mechanics
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