1).a) Show that the bound state wave function ψb (Eqn 2.129) and
the continuum state wave
function ψk (Eqn 2.131-132 with coefficients 2.136-137) are
orthogonal, i.e., 〈ψb|ψk〉 = 0. (b)
[bonus] Explain why the orthogonality exists, example as, are they
eigenstates of an operator? If so,
what is the operator? If not explain.
Show that the deuteron has no bound excited states by estimating
the excited state energy and comparing it to the potential well.
Consider two cases for the excited state:
a) higher order radial eigenfunctions,
b) non-zero angular momentum.
c) If the nuclear force had a longer range R >R0 we could
possibly have excited states. What would be the minimum and maximum
values of R∗ so that there could be an excited state with l = 1 but
no excited...
An electron is bound to a finite potential well. (a) If the
width of the well is 4 a.u., determine numerically the minimum
depth (in a.u.) such that there are four even states. Give the
energies of all states including odd ones to at least 3 digits. (b)
Repeat the calculation, but now keep the depth of the well at 1
a.u., determine the minimum width (in a.u.)
Consider two electrons, both in the ground state of an in?nite
potential well. Write the wave function ?(x1,x2) for this
system.
Assume the electrons are non-interacting
In 1-D, the finite square well always has at least one bound
state, no matter how shallow the well is. In 3-D, a finite-depth
well doesn't always have a bound state.find bound states
Sketch the wave-function of the ground state of a particle of
mass m which is con- fined in one dimension within a square
potential well of infinite height, centred at x = 0 and of width a
between x = ?a/2 and x = a/2.
What type of function is that?
If the infinite potential well is replaced by a potential well
of finite height, sketch the new ground state
wave-function. Explain qualitatively how the
ground state energy changes in...
1.Normalize the wave function for a particle in infinite
potential well?
2.What is the Tunnel effect? Calculate depth of penetration in a
potential barrier-Which attenuation is to be used as standard for
this calculation?