Question

A system consists of two particles, each of which has a spin of 3/2. a) Assuming the particles to be distinguishable, what are the macrostates of the z component of the total spin, and what is the multiplicity of each? b) What are the possible values of the total spin S and what is the multiplicity of each value? Verify that the total multiplicity matches that of part (a). c) Now suppose the particles behave like indistinguishable quantum particles. What is the multiplicity of each of the macrostates of the z component of the total spin? d) Show that for these quantum paricles it is possible to have only combinations with total spin S=3 or 1.

Answer #1

Consider the states of the combined total spin of two particles,
each of which has spin 5/2 with ms= +5/2, +3/2,
+1/2, −1/2, −3/2, and −5/2.
(a) How many macrostates are there corresponding to the
different values of the total spin if the particles are
distinguishable?
(b) If the two particles are distinguishable, what is the total
number of microstates for all the allowed macrostates?
(c) If the two particles are indistinguishable, what is the
total number of microstates for...

Six identical but distinguishable particles share seven units
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A system consists of two particles. The first particle has mass
m1 = 2.0 kg and a velocity of (-5.0 i+1.0j)
m/s, and the second particle has mass m2 = 1.00
kg and a velocity of (1.0i - 5.0j) m/s. A:) What is
the velocity of the center of mass of this
system?
B:) what is the total momentum of this system?

Given S 1 = 2 and S 2 = 2, write the state | 3 , 1 >
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value?

Two particles with masses ?1 = 3 ?? and ?2 = 2 ??, which slide
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1) The Pauli Exclusion Principle tells us that
no two electrons in an atom can have the same four quantum
numbers.
Enter ONE possible value for each quantum number of an electron
in the orbital given.
Orbital
n
l
ml
ms
1s
There are a total of values possible for
ml.
2s
There are a total of values possible for
ml.
2) The Pauli Exclusion Principle tells us that
no two electrons in an atom can have the same four...

1. Consider the problem of two polluting sources in the region,
each of which generated 10 units of pollution for a total of 20
units released into the environment. The government determined that
emissions must be reduced by 12 units across the region to achieve
the ”socially desirable level of pollu- tion”. Each firm faces
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Polluter 2, marginal abatement cost is...

Consider a city with three consumers:1, 2, and 3. The city
provides park land for the enjoyment of its residents. Parks are a
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consumers are as follows:
D1=40-z
D2=30-z
D3=20-z
These formulas give the height of each consumer's demand curve
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Multiple Choice
Select the best answer from the available choices for each
question.
Which of the following is NOT part of the definition of
a sample space S?
S can be discrete or continuous
Each outcome must be in S at most once
Each element in S is equally likely
Each outcome must be in S at least once
S is a set of possible outcomes in an experiment
Three A’s, three B’s, and two C’s are arranged at
random...

Do the following problems. 1. Each of three barrels from a
manufacturing line are classified as either above (a) or below (b)
the target weight. Provide the ordered sample space. 2. The heat on
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ordered sample space. 3. Consider the set of Beatles songs with a
primary writer as either Paul McCartney (P) or John...

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