Write a comparative essay, on the perturbation theory, the
variational principle and the WKB approximation, including their
applications in quantum mechanics.
How is the variational principle applied?
Question 3 options:
a)
To find an upper bound for the ground-state kinetic energy
b)
To find an upper bound for the ground-state potential
energy
c)
To find a lower bound for the ground-state kinetic energy
d)
To find a lower bound for the ground-state potential
energy
e)
To find an upper bound for the ground-state total energy
Q1
What is the difference between the linear variational method and
more "traditional" variational method for approximating
eigenstate
and energies. How does this affect the approach to minimize the
variational energy?
Q2
What are the Secular Equations? What is the Secular determinant?
What is the difference? Does solving one affect the need to solve
the
other?
a. What is the principle of “original horizontality”
b. What is the principle of superposition?
c. What can pieces of an older rock being included in the layer
above it tell you?
d. What is the
principle of cross cutting relationships?
e. What is an
unconformity?
F. What is a disconformity and how would it form?
g. What is a nonconformity and how would it form?
h. What is an angular unconformity and how would it form?
Consider the asymmetric 1/2 harmonic oscillator. use the
Variational Principle to estimate the ground state energy of this
potential. Use as your trial function Axe^bx^2
a. What is the First Principle in the Code of Professional
Conduct of Engineers?
b. What is whistleblowing? Does it
contradict the principle of confidentially considerations?
c. What is Conflict of Interest? Give
an example.
Explain the variational approach to finding approximate
eigenenergies of a Hamiltonian. What are the advantages and
disadvantages of this approach compared to the time independent
perturbation theory. Explain the single parameter variational
method and the linear combination of states method.
What are the ways that influenza virus (a) conforms to
the principle of genetic economy, (b) manages to have all cistrons
expressed, (c) controls the level of gene product that it generated
and (d) interacts with and takes over the host gene expression
machinery? Explain each of these.
(a.) What is the underlying principle of valuation? (3)
(b). Why is it critical for us to learn the concept of
(security) valuation? (3)
(a). What is a bond, who buys/sells them, and why? (2+2+2)
(b). What are the five characteristics of a typical bond?
(5)
What cash flow(s) are expected by bondholders? Why is bond a
“fixed income” security? (2+1)