I 5. Suppose that a wavefunction is given by. 0 v (e,t) = { = { t < 0 expli(kx- (ER- iT/2)t/h)] t≥0' where ER and I> 0 are parameters. (a) What is y(x, t)|2 for t≥ 0? Note that this wavefunction could represent that of state (or particle) produced at time t = 0 which decays with a mean lifetime of T = ħ/T. (b) This wavefunction can be transformed the the energy domain via a Fourier Transform: Þ(x, E) = What is Þ(x, E) ? 1 √2V(x, t) expli(Et/h)] dt. 2π
I 5. Suppose that a wavefunction is given by. 0 v (e,t) = { = { t < 0 expli(kx- (ER- iT/2)t/h)] t≥0' where ER and I> 0 are parameters. (a) What is y(x, t)|2 for t≥ 0? Note that this wavefunction could represent that of state (or particle) produced at time t = 0 which decays with a mean lifetime of T = ħ/T. (b) This wavefunction can be transformed the the energy domain via a Fourier Transform: Þ(x, E) = What is Þ(x, E) ? 1 √2V(x, t) expli(Et/h)] dt. 2π
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I need help with question 5 part a and b.
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5. Suppose that a wavefunction is given by.
0
t<0
v(x,t) = { expli(ka - (En-iT/2)t/h)] +20
where ER and I >0 are parameters.
(a) What is y(x, t) |2 for t≥ 0? Note that this wavefunction could represent
that of state (or particle) produced at time t = 0 which decays with a
mean lifetime of T = ħ/T.
(b) This wavefunction can be transformed the the energy domain via a Fourier
Transform:
Þ(x, E) =
1
-∞
(x, t) expli(Et/h)] dt.
What is P(x, E) ?
(c) What is P(x, E)|2 ? Plot it. The parameter I is called the Full Width
at Half Maximum (FWHM). Does this make sense? Note that I'r = ħ is
a particular case of the uncertainty principle that is an exact relation. It
holds for states which decay according the exponential decay law (which is
often the case, due to decay rates being constant). It implies that unstable
states (or particles) necessarily have a finite energy width.
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Transcribed Image Text:I
5. Suppose that a wavefunction is given by.
0
t<0
v(x,t) = { expli(ka - (En-iT/2)t/h)] +20
where ER and I >0 are parameters.
(a) What is y(x, t) |2 for t≥ 0? Note that this wavefunction could represent
that of state (or particle) produced at time t = 0 which decays with a
mean lifetime of T = ħ/T.
(b) This wavefunction can be transformed the the energy domain via a Fourier
Transform:
Þ(x, E) =
1
-∞
(x, t) expli(Et/h)] dt.
What is P(x, E) ?
(c) What is P(x, E)|2 ? Plot it. The parameter I is called the Full Width
at Half Maximum (FWHM). Does this make sense? Note that I'r = ħ is
a particular case of the uncertainty principle that is an exact relation. It
holds for states which decay according the exponential decay law (which is
often the case, due to decay rates being constant). It implies that unstable
states (or particles) necessarily have a finite energy width.
Q Search
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