5. Consider a particle in a two-dimensional, rigid, square box
with side a. (a) Find the time independent wave function
φ(x,y)describing an arbitrary energy eigenstate. (b)What
are the energy eigenvalues and the quantum numbers for the three
lowest eigenstates? Draw the energy level diagram
Use the one-dimensional particle-in-a-box model with
impenetrable walls and the equation R = R_0*A^(1/3) to estimate the
minimum kinetic energy of a nucleon in a nucleus. Express your
answer in MeV and in terms of a number 'n' the mass number 'A', and
an exponent p, which is the ratio of two integers, resulting in K =
n/A^p.
Consider a particle of mass m confined to a
one-dimensional box of length L and in a state with normalized
wavefunction. For a partide in a box the energy is given by
En =
n2h2/8mL2
and, because the potential energy is zero, all of this energy is
kinetic. Use this observation and, without evaluating any
integrals, explain why < px2>=
n2h2/4L2
Use the quantum particle wavefunctions for the kinetic energy
levels in a one
dimensional box to qualitatively demonstrate that the classical
probability distribution
(any value of x is equally allowed) is obtained for particles at
high temperatures.
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
Write a function to solve the two-dimensional in Matlab,
unsteady heat conduction equation with no internal heat generation
on a square domain. The length of each side of the square is 1 m.
The function will have the following 4 inputs:
npts
number of grid points in each coordinate direction
nt
number of time steps to take
dt
size of time step (s)
alpha
thermal diffusivity (m2/s)
Use the following initial and boundary conditions:
Initialize the body to T =...
Consider a particle of mass m that can move in a one-dimensional
box of size L with the edges of the box at x=0 and x = L. The
potential is zero inside the box and infinite outside.
You may need the following integrals:
∫ 0 1 d y sin ( n π y ) 2 = 1 / 2 , for all
integer n
∫ 0 1 d y sin ( n π y ) 2 y = 1...