We consider an experiment in which the position is accurately known at the beginning and the momentum is measured. We shall see that the measurement gives an inaccurate momentum but also introduces an uncertainty into the position.
We assume that the particle is an atom in an excited state,
which will give off a photon that has the frequency if the
atom is at rest.Because of the doppler effect, motion of the atom
toward the observer with speed v means that the observed frequency
is given approximately by
so that
.
Accurate measurement of the momentum mv by measurement of the
frequency requires a
relatively long time
; the minimum error
in the frequency measurement can be shown to be
.
The instant at which the photon is emitted is uncertain by
;
at this instant the momentum of the atom decreases by
,
and its velocity decreases by
. This makes
the subsequent position of the atom uncertain by the amount
eq 1).since the later the photon is emitted, the longer the atom
has the higher velocity and the farther it would have
travelled.
This position uncertainty is because of the finiteness of
.
The momentum uncertainty is
eq 2).
The combination of eq 1) and eq 2) leads to Heisenberg's uncertainty relation.
Problem 6 If you have a quantum system and perform a single measurement in which you measure the observable property associated with an operator Å, what will you measure? no further information given on the question
What is the quantum measurement problem? Explain one proposed solution to that problem, in under 2000 words.
Describe quantum measurement processes.
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Briefly explain the meaning of the following terms: (i) primary photochemical process (ii) quantum yield (iii) Stark-Einstein law (iv) active medium (v) optical feedback
This is quantum chemistry. Please explain the answer. Thank you.
4. A hydrogen atom is in a state that is given by (a). Is ψ an eigenfunction of the Hamiltonian for this system? If so, what is the eigenvalue? (b). If a measurement is made of the value of 12 for this system, what are the possible results of the measurement? (c). What is the probability of obtaining each of the results for 12 that you found in (b)? (d)....
Which best describes "measurement" in quantum mechanics? a) An event that collapses the wave function of a particular entity b) An event that produces information c) An event that determines the probability of a given state d)An event that is local e) An event that contains no hidden variables
17. Assume the measurement we conduct follows Poisson Distribution model. We have a single measurement x sa 100, then what is the best estimate of the deviation from the true mean? A. 5%; (B. 10% C. 10 D . 1.
3. (a) What is the difference between the signal measurement methods in differential mode' vs 'single ended measurement"? (b). A 14 bit A to D converter is to be employed with an Iron-constantan thermocouple. What temperature resolution can be expected with a full scale voltage of 100 mV? Thermocouple shows 0.5 mV at 50°C and 3.052 mV at 100°C.
3. (a) What is the difference between the signal measurement methods in differential mode' vs 'single ended measurement'? (b). A 14 bit A to D converter is to be employed with an Iron-constantan thermocouple. What temperature resolution can be expected with a full scale voltage of 100 mV? Thermocouple shows 0.5 mV at 50°C and 3.052 mV at 100°C.