For a particle described by the wavefunction in Equation (1), show that the expectation values for momentum and momentum-squared are given by shown in image b) For the same particle, show that the expectation values for position and position-squared are given by shown in image
For a particle described by the wavefunction in Equation (1), show that the expectation values for momentum and momentum-squared are given by shown in image b) For the same particle, show that the expectation values for position and position-squared are given by shown in image
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Question
a) For a particle described by the wavefunction in Equation (1), show that the expectation
values for momentum and momentum-squared are given by
shown in image
b) For the same particle, show that the expectation values for position and position-squared are given by
shown in image
Transcribed Image Text:a)
For a particle described by the wavefunction in Equation (1), show that the expectation
values for momentum and momentum-squared are given by
(p) = 0
(x)
and
=
b)
For the same particle, show that the expectation values for position and position-squared
are given by
(p²)
0 and
ħ²π²
L²
1
2
(2²) = ²/2 (²3 - ²/3).
4
Transcribed Image Text:The following two questions refer to the wavefunction of a particle in the groundstate of an infinite
square well with walls at x = L/2 and x = -L/2. This wavefunction can be written as
V₁(t, x) = √√/²/₁
COS
(1₂)
e-iEt/ħ
(1)
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