Ehrenfest theorem states that the time evolution of the expectation values of position and momentum obey classical laws d(r) d(p) (P), dt A more general form derived by Heisenberg is (4) = ((A4, H)) + (34) where A is some quantum mechanical operator and H is the Hamiltonian operator H= +V(x, t) 2m also, [A, H] = AH - HA. (a) Using the general form of the Ehrenfest theorem, show that dip) - (-5) = (F) dt (b) Also show that m
Ehrenfest theorem states that the time evolution of the expectation values of position and momentum obey classical laws d(r) d(p) (P), dt A more general form derived by Heisenberg is (4) = ((A4, H)) + (34) where A is some quantum mechanical operator and H is the Hamiltonian operator H= +V(x, t) 2m also, [A, H] = AH - HA. (a) Using the general form of the Ehrenfest theorem, show that dip) - (-5) = (F) dt (b) Also show that m
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![2.
Ehrenfest theorem states that the time evolution of the expectation values of
position and momentum obey classical laws
d(x)
d(p)
m = (p),
= (F)
dt
dt
A more general form derived by Heisenberg is
(A) = ({A, H])+
Ət
where A is some quantum mechanical operator and H is the Hamiltonian operator
H =
p²
2m
+V(x, t)
also, [A, H] = AH - HA.
(a) Using the general form of the Ehrenfest theorem, show that
d(p)
P) = (-3) = (F)
dt
(b) Also show that
d
1
(P)
m
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6d625ab-782a-45d3-ae83-791ae5efe87b%2Fbc477323-aa10-437b-8ac1-a979d4ef5b32%2Fqy5mmmr_processed.png&w=3840&q=75)
Transcribed Image Text:2.
Ehrenfest theorem states that the time evolution of the expectation values of
position and momentum obey classical laws
d(x)
d(p)
m = (p),
= (F)
dt
dt
A more general form derived by Heisenberg is
(A) = ({A, H])+
Ət
where A is some quantum mechanical operator and H is the Hamiltonian operator
H =
p²
2m
+V(x, t)
also, [A, H] = AH - HA.
(a) Using the general form of the Ehrenfest theorem, show that
d(p)
P) = (-3) = (F)
dt
(b) Also show that
d
1
(P)
m
=
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