So this course is on advanced quantum mechanics
and its applications.
So we will see various advanced topics in
quantum mechanics and their applications in
various fields of topical interests which
are very important and of research interest
these days.
So the course starts with the basic introduction
to the birth of quantum mechanics or the postulates
that the quantum mechanics had to offer and
different representations of quantum mechanics
such as Heisenberg interaction representation
and Schrodinger representation.
Will also learn Heisenberg’s uncertainty
principle and how it has been applied to various
problems.
Then, the density matrix formalism, the quantum
harmonic oscillator using the raising and
the lowering operators and their applications
to quantum optics such as coherent states
and squeeze states will also learn symmetries
and conservation laws of quantum mechanics.
Also this course would be on the various solutions
of Schrodinger equations for various kinds
of potentials such as spherically symmetric
potentials.
One of the simple examples of such things
is in hydrogen atom, which consist of one
electron and a proton at the nucleus.
Will also learn the spherical oscillator in
3 dimensions and the degeneracies.
These things would be applied to quantum dots
and also we shall discuss the technology that
involved therein.
We shall then do the orbital and spin angular
momentum.
We will learn how to calculate the Clebsch–Gordan
coefficients then the hyperfine interaction
and the spin dipolar interaction especially
in the context of quantum gases and applications
of these different topics of angular momentum
for NMR the nuclear magnetic resonance and
we shall also take a very detail study on
quantum information theory, the quantum measurement,
EPR, paradox and Bell’s inequalities.
Then starting with cubits and quantum circuits
will go on to discuss Shannon entropy, classical
and quantum computations, algorithms, error
calculations etc.
Then, we also would do periodically driven
systems, the quantum dynamics therein and
the correlations especially for two level
systems and these chaotic trajectories that
evolve there and different roots to chaos
and finally we would learn about the proximate
methods of solving Schrodinger equation where
exact solutions are not available.
And will do a perturbation theory time dependent
and time independent and will see various
examples or applications such as Zeeman effect,
Stark effect and computing the Einstein’s
AB coefficients for lasers and will also do
variational calculations.
So where the smallness of the perturbing term
is not clear then we can do a variational
theory and where we actually write down the
variational wave function which satisfies
the boundary conditions in terms of some free
parameters called as variational parameters.
And then the energy is minimized with respect
to that variational parameter and will also
do WKB approximation, Wentzel–Kramers–Brillouin
approximation mainly for the linear potentials
and will also give a sufficiently elaborate
introduction to time dependent perturbation
theory as well and look at various applications
that are involved there.
