Explain what is physically meant by “Degrees of Freedom” and the
“Equipartition Theorem”.
a. Degrees of...
Explain what is physically meant by “Degrees of Freedom” and the
“Equipartition Theorem”.
a. Degrees of freedom refers to the number of rights, or
freedoms, a person exercises in a given partition of time, after
their yearly schedules have been equally partitioned into
appropriate chunks of time.
b. The Equipartition theorem states that every atom in a solid
has a specific heat equal to kB/2 for every degree of
freedom (or allowed kind of motion).
c. The Equipartition theorem states...
A
system, at temperature T, has particles that can be in three
different states: s=-1, 0,...
A
system, at temperature T, has particles that can be in three
different states: s=-1, 0, 1. The energy of the particle is given
by: E_s = -μ*B*s , where μ is a constant and B is an applied
magnetic field.
(a) Find the expected energy value for a system of 3
particles.
(b) Generalize part (a) for a system of N particles
Imagine there exists a third type of particle which can share a
single-particle state with one...
Imagine there exists a third type of particle which can share a
single-particle state with one other particle of the same type but
no more. There is a system in contact with a reservoir of the
particles, which are allowed to move back and forth to the system.
There is a single energy level available in the system. When a
particle occupies this level, its energy is ε.
What are the the possible states of the system, and what is...
A system consists of two particles, each of which has a spin of
3/2. a) Assuming...
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...
Consider the states of the combined total spin of two particles,
each of which has spin...
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...
Consider a system that contains N sites. Each site may be empty,
or may be occupied...
Consider a system that contains N sites. Each site may be empty,
or may be occupied by a
spin 1 particle. A spin 1 particle may be in one of three states
(Sz=1,0,-1). Please compute
(a) The total number of states
(b) The entropy, if all states are accessible
(c) The most probable value of the number of occupied states.
(d) The entropy, if the only accessible states are those in which
1/3 of the sites are occupied.
Here please...
N particles can move in plane (x,y).
Write down coordinates and momenta of all particles forming...
N particles can move in plane (x,y).
Write down coordinates and momenta of all particles forming the
phase space and determine number of degrees of freedom
s.
(a) x1, px1,
y1, py1,
x2, px2,
y2, py2,…,
xN, pxN,
yN, pyN ,
s=2N
(b) x1, px1,
x2, px2, …,
xN, pxN ,
s=2N
(c) y1, py1,
y2, py2,…,
yN, pyN ,
s=2N
(d) x1, y1,
x2, y2, …,
xN, yN ,
s=2N
and why you choose
We observe 3 particles and 3 different one-particle states
ψa(x), ψb(x) i ψc(x). How many
different...
We observe 3 particles and 3 different one-particle states
ψa(x), ψb(x) i ψc(x). How many
different states that describe a system of three particles can we
make:
(a) if the particles can be distinguished;
(b) if the particles are identical bosons;
(c) if the particles are identical fermions?
Note that, unlike the exercise task, there is a possibility that
the particles may be in the same quantum state.
For example, ψ(x1, x2, x3) =
ψa(x1)ψa(x2)ψc(x3)