Please explain how symmetries in quantum mechanics work, how
they impact eigenenergies and eigenstates of the...
Please explain how symmetries in quantum mechanics work, how
they impact eigenenergies and eigenstates of the Hamiltonian, how
symmetries are identified, and how they can be exploited. Explain
rotational symmetry and how it works.
Solutions
Expert Solution
Soln:
Symmetry in quantum mechanics is explained.Eigen states and
eigen values are explained.
I have a question about difference between physical observables
and eigenstates in quantum mechanics
it is postulated in Quantum Mechanics that
physical observable in Classical Mechanics are represented by
linear operators
the state of the particle was represented by a curve in phase
space determined by generalized position and momentum
but in Quantum Mechanics it is represented by a vector in
Hilbert space
and if we measure the physical observable of the particle, the
previous state of the particle once...
A.
Describe specifically two major differences between quantum
mechanics and classical mechanics.
B. How does the correspondence principle link quantum
mechanics and classical mechanics?
C. Why is it still accurate to use classical mechanics for
human size objects? That is, why are our wave like properties not
observed?
Explain:
(5) a. Why quantum mechanics is
needed by describing a relevant
experimental result (not Young’s experiment).
(Please just point out the
particular experimental feature or features relevant to the need of
quantum mechanics and do not discuss the experimental
setups.)
Discuss TWO of the following approximation methods in quantum
mechanics. Explain the types of problems to which the approximation
methods can be applied, how the basic theory is developed, and how
they are applied in practice. Include some mathematical details in
your answer.
(i) The Hartree theory of atoms and ions.
(ii) The variational method.
(iii) Non degenerate and degenerate perturbation theory.
Using the arguments based on quantum mechanics and the
Boltzmann energy distribution
explain briefly:
a) why real molecules behave (from the thermodynamics point of
view) as the ideal gas molecules?
b) Why are the rotational degrees of freedom activated at lower
temperatures for most molecules?
c) Why are the vibrational degrees of freedom activated at high
temperatures for most molecules?
d) Why are the noble gases well approximated by the ideal gas?