In 1-D, the finite square well always has at least one bound
state, no matter how...
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
Consider our graphical analysis of the bound states in a finite
square well of depth V0 and width a.
Determine
a) The condition on V0 and a that there is
at most one bound state in the problem.
b) The condition on V0 and a that there is
at most four bound states in the problem.
c) Suppose the potential parameters are such that the third
bound state is just barely bound. What can you say about the
binding energy...
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.)
In elementary quantum mechanics, the square well is used to
model the behavior of a bound particle in which one or more forces
(external potentials, interaction with other particles, etc)
prevent or restrict its ability to move about. We have seen in
class that the solutions to the Schrodinger equation in and around
the quantum well result in a series of eigenvector wavefunctions
with distinct energy levels. In this assignment, we will use MATLAB
to create the system and experiment...
A particle in an infinite one-dimensional square well is in the
ground state with an energy of 2.23 eV.
a) If the particle is an electron, what is the size of the
box?
b) How much energy must be added to the particle to reach the
3rd excited state (n = 4)?
c) If the particle is a proton, what is the size of the box? d)
For a proton, how does your answer b) change?
Consider two non-interacting particles in an infinite square
well. One is in a state ψm, the other in a state
ψn with n≠m. Let’s assume that ψm and
ψn are the ground state and 1st excited state
respectively and that the two particles are identical fermions. The
well is of width 1Å. What is the probability of finding a particle
in the 1st excited state in a region of width 0.01Å?
Does this change if the particles are distinguishable?
A system of N identical, non-interacting particles are placed in
a finite square well of width L and depth V. The relationship
between V and L are such that only 2 bound states exist. What is
this relationship? Hint: What is the requirement on E for a bound
state? For these two bound states, what is the expected energy of
the system as a function of temperature? The result only applies
when T is low enough so that the probability...
Question 1. CHI-SQUARE Technique
a. Describe the purpose of the Chi-Square Technique.
b. State at least two research problems or question that
requires the use of the Chi-Square Technique
c. Identify, describe and test the assumptions related to the
Chi-Square technique
d. State examples of the Chi-Square technique outcomes
e. State examples of Chi-Square technique report results
Question 1. CHI-SQUARE Technique a. Describe the purpose of the
Chi-Square Technique.
b. State at least two research problems or question that
requires the use of the Chi-Square Technique
c. Identify, describe and test the assumptions related to the
Chi-Square technique
d. State examples of the Chi-Square technique outcomes
e. State examples of Chi-Square technique report results
An electron is in the ground state of an infinite square well.
The energy of the ground state is E1 = 1.35
eV.
(a) What wavelength of electromagnetic radiation would be needed
to excite the electron to the n = 4 state?
nm
(b) What is the width of the square well?
nm