For the one dimensional Ising model with N particles in the
canonical ensemble compute
the chemical...
For the one dimensional Ising model with N particles in the
canonical ensemble compute
the chemical potential of the system assuming it is in the
canonical ensemble.
Given the Ising model or a canonical ensemble how is
the critcal temperature calculated?
Also, would you happen to know the relationship
between how many neighbor interactions there are and how this
affects temperature?
thanks!
What is the length of a one-dimensional box in which an electron
in the n = 1, state has the same energy as a photon with a
wavelength of 600 nm? What is the energy of n = 2 and n =3 state?
What energy of a photon, if absorbed by the electron could move it
from the n = 1 state to the n = 2 state? Write legibly.
Consider a system of three non-interacting particles confined by a
one-dimensional harmonic oscillator potential and in thermal
equilibrium with a total energy of 7/2 ħw.
(a) what are the possible occupation numbers for this system
if the particles are bosons.
(b) what is the most probable energy for a boson picked at
random from this system.
2. For a system of non-interacting, one-dimensional,
distinguishable classical particles in a harmonic oscillator
potential, V = kx2 in contact with a particle
reservoir with chemical potential µ and a thermal
reservoir at temperature T.
(a) Calculate the grand partition function Z for the system.
Note that there is no fixed "volume" for this system.
(b) Obtain N (number of particles) and U as functions of µ and T
and show that U satisfies the equipartition theorem
Create a function to output a one dimensional double array M
with n elements where the first three elements are 1 and each
subsequent element is the sum of previous three elements before it.
Name the function myArray. Write the function in the correct format
to be used to create a Matlab function. Call the function in
correct format to output the array with 7 elements.
Consider the one dimensional model of one-particle-in-a-box. Under
what condition the two quantum levels are orthogonal. Namely, find
the relation between m and n so that < m | n > = 0
Imagine a gas of N spherical particles that are free to
distribute throughout either a large volume or a small one. Why
does the gas spread out into a large volume? The tendency to spread
out is pressure and can be explained in terms of multiplicity or
increased probability. To illustrate this, let's create a simpler
model that we can visualize, solve exactly, and will illustrate the
essence of the problem without the mathematical complexity. For
each of the following,...
Suppose we model a golf club hitting a stationary golf ball as a
one-dimensional elastic collision between the moving club and the
stationary ball. Suppose the golfer can swing the club so that the
0.200 kg head has a velocity of 48 m/s when it strikes the ball of
mass 0.045 kg.
Determine the speed of the ball after the collision.
If the golfer uses a heavier mass club, one with double the
mass, and was able to swing with...
In the Bohr model, when an electron leaves one n orbit and
enters another n orbit, a photon is either emitted or absorbed.
Derive a relationship between the wavelength of the emitted or
absorbed photon and the change in the DeBroglie wavelength of the
electron when it moves from one n to another n.