If a particle’s momentum uncertainty, what is the uncertainty in
its position. Very briefly, what does this result mean?
What is the Compton effect? What is measured in observations of
the Compton effect? How does this differ from the expectations of
classical physics? At what condition for incident radiation can the
effect be observed? What important property of light does the
Compton effect demonstrate? How does it give evidence of
electromagnetic radiation`s particle nature?
A 12 gram bullet leaves the barrel of a rifle at 180 m/s. If the vertical position of the bullet is known to a precision of 0.65 cm (radius of the rifle's barrel). What is the minimum uncertainty in the bullet's vertical momentum?
The most basic explanation for the Heisenberg Uncertainty
Principle is that the momentum and position of a quantum particle
is not very distinct when an attempt is made to measure them
together. But what is it that causes the uncertainty? Because if
there is no change in the momentum, then it would be the same as
measuring the two separately. So what causes this change in the
instantaneous perceived momentum. A change in mass? Velocity? Or
net composition of the...
particle in a well
1. Using the uncertainty principle for position and momentum,
estimate the ground state energy
for an infinite well of width a, compare the obtained result with
the one found in the lecture.
2. Compute <p> and <x> for the particle in a box.
3. Prove that the eigenfunctions ψn(x) are orthogonal .
4. What are the energies of the ground state, first excited and
second excited states for an
electron trapped in an infinite well of...
Exercise 6:
A) How does the Heisenberg Uncertainty (with momentum and
position) force us to abandon a deterministic universe?
B) In what important ways is the Bohr model of the atom
incompatible with quantum theory? Include the concept of orbits and
what is known about angular momentum.
1. What is the momentum (p) of a 960-MeV proton
(that is, its kinetic energy is 960 MeVMeV )?
Express your answer with the appropriate units.
2. An electron (mmm = 9.11×10−31 kg
) is accelerated from rest to speed vv by a conservative force. In
this process, its potential energy decreases by
6.70×10−14 JJ . Determine the electron's speed, v. (in
term of c.)
An object is moving along a straight line, and the uncertainty
in its position is 2.20 m. (a) Find the minimum uncertainty in the
momentum of the object. Find the minimum uncertainty in the
object's velocity, assuming that the object is (b) a golf ball
(mass = 0.0450 kg) and (c) an electron.
Governments artificially keep minimum wage above equilibrium,
and in some cases, keep rent payments below the market equilibrium.
What are the ramifications of a too high minimum wage and a too low
rent payment? Provide examples of the pros and cons of each
scenario.
What is the uncertainty of the position of the bacterium?
Express your answer with the appropriate units.
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A student is examining a bacterium under the microscope. The
E. coli bacterial cell has a mass of m = 1.10 fg
(where a femtogram, fg, is 10−15g) and is swimming at a velocity of
v = 9.00 μm/s , with an uncertainty in the
velocity of 7.00 % . E. coli bacterial cells are around 1
μm ( 10−6 m) in...
2a. Confirm that the position and
momentum, p=-ℏ ∂/∂x, operators
do not commute.
2b. Show how the statement above
limits the ability for a state that to be both an eigenstate of
position and momentum concurrently.
2c. For an eigenstate where the
momentum is zero, show that x than p leads to a result, xp, that is
different than that of p then x.