Question

Consider a two-dimensional squared-well of dimensions *L*
× *L*. The length L is such, that the ground state energy of
one electron confined in this box is 0.1eV.

(a) Write down the 5 lowest energy states and their
corresponding degeneracy (your energy values must all be
different!) and label them E_{1} · · · E_{5}

(b) If the electron finds itself in one of the states with
energy E_{5}, how much energy would be required to lift the
electron from E_{5}, to the next lowest energy level
E_{6}?

Answer #1

Consider a two-dimensional squared-well of dimensions L
× L. The length L is such, that the ground state energy of
one electron confined in this box is 0.1eV.
(a) Write down the 5 lowest energy states and their
corresponding degeneracy (your energy values must all be
different!) and label them E1 · · · E5
(b) If the electron finds itself in one of the states with
energy E5, how much energy would be required to lift the
electron from...

Exercise
3. Consider a particle with mass m in a
two-dimensional infinite well of length L, x, y
∈ [0, L]. There is a weak potential in the well
given by
V (x,
y) = V0L2δ(x −
x0)δ(y − y0)
.
Evaluate the first order correction to the energy of the ground
state.
Evaluate the first order corrections to the energy of the first
excited states for x0 =y0 = L/4.
For the first excited states, find the points...

Eight electrons are confined to a two-dimensional infinite
potential well with widths L_X = L y =L. Assume that the electrons
do not electrically interact with one another. Considering electron
spin and degeneracies of some energy levels, what is the total
energy of the eight-electron system in its ground state, as a
multiple of h^2/(8mL^2 )?

An electron is trapped in an infinite one-dimensional well of
width = L. The ground state energy for this electron is 3.8
eV.
a) Calculated energy of the 1st excited state.
b) What is the wavelength of the photon emitted between 1st
excited state and ground states?
c) If the width of the well is doubled to 2L and mass is halved
to m/2, what is the new 3nd state energy?
d) What is the photon energy emitted from the...

If an electron is confined to one-dimensional motion
between two infinite potential walls which are separated by a
distance equal to Bohr radius, calculate energies of the three
lowest states of motion.Calculate numerical value of ground state
energy and compare it with hydrogen atom ground state energy.

Consider a three dimensional rectangular infinite potential well
with sides of length L, 2L and 3L.
What is the energy of the first excited state relative to the
energy of the ground state?
What is the energy of the second excited state relative to the
energy of the ground state?
What is the energy of the third excited state relative to the
energy of the ground state?
What is the energy of the fourth excited state relative to the
energy...

An electron is in an infinite one-dimensional square well of
width L = 0.12 nm.
1) First, assume that the electron is in the lowest energy
eigenstate of the well (the ground state). What is the energy of
the electron in eV? E =
2) What is the wavelength that is associated with this
eigenstate in nm? λ =
3) What is the probability that the electron is located within
the region between x = 0.048 nm and x =...

If an electron is confined to one-dimensional motion between two
infinite potential walls which are separated by a distance equal to
the Bohr radius, calculate the energies of the three lowest states
of motion. Calculate numerical value of ground state energy and
compare it with hydrogen atom ground state energy.

II(20pts). Short Problems
a) The lowest energy of a particle in an infinite one-dimensional
potential well is 4.0 eV. If the width of the well is doubled, what
is its lowest energy?
b) Find the distance of closest approach of a 16.0-Mev alpha
particle incident on a gold foil.
c) The transition from the first excited state to the ground
state in potassium results in the emission of a photon with = 310
nm. If the potassium vapor is...

A one-dimensional impenetrable box of length a contains an
electron that suffers a small perturbation and emilts a photon
frequency
v=3E1/h
where E1 energy of the grounfd state. From this would
it be correct to conclude that the initial state of the electron is
the n = 2 box state? why or why not?

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