Dr. Aniruddha Chakraborty

School of Basic Sciences

Indian Institute of Technology Mandi

Kamand, Himachal Pradesh 175005

India

ph: +(91)1905-237930

achakrab

*Assignment 1*

Find the Reflection and the Transmission probability for the following two step potentials

(a) if x <0, V(x)=0, otherwise V(x) = - V and

(b) if x <0, V(x)= - V, otherwise V(x) = 0.

*Assignment 2*

Find the Reflection and the Transmission probability for the following two step potentials

(a) For t < 0, if x < 0, V(x) = 0, otherwise V(x) = V.

At t = 0, the potential is suddenly changed to the following

if x<0, V(x) = 0, otherwise V(x ) = - V.

(b) For t < 0, if x < 0, V(x) = 0, otherwise V(x) = V.

At t = 0, the potential is suddenly changed to the following

if x < a, V(x) = 0, otherwise V(x) = V, where 'a' is a positive number.

(c) For t < 0, if x < 0, V(x) = 0, otherwise V(x) = V.

At t = 0, the potential is suddenly changed to the following

if x < a, V(x) = 0, otherwise V(x) = - V, where 'a' is a positive number.

*Assignment 3*

1. Find the Transmission and Reflection probability for for the Dirac delta potential problem.

2. Find the Transmission and reflection probability for the oscillating (strength) Dirac delta potential problem.

*Assignment 4*

1. In a rectangular potential barrier problem, derive analytical expressions for transmission and reflection probabilities at E = V ?

2. In a particle in a box (of length L) problem, suppose the system is in ground state at time t=0. Now if the length of the box is suddenly changed to 2L at time t= t', what is the probability of finding the system at the ground state of the new Hamiltonian at time t (t > t') ?

*Literature Survey*

Do a literature survey any research area of your choice related to 'Theoretical Chemistry' and submit a brief report which should include

(a) reference of at least 10 research papers &

(b) information of at least 10 research groups.

*Reading Assignment*

Study & understand and then submit a brief report on the following topic -

“Can temperature be defined when the system is not in thermodynamic equilibrium”.

*Short Project*

Choose a problem related to 'Theoretical Chemistry', solve it using Mathematica and submit a brief report along with the Mathematica notebook.

*Interactive Assignment*

** Topic:** Quantum Mechanics of Hydrogen Atom - Numerically

Time Duration: One Month.

Students are expected to solve this assignment with the help of Instructor, they are allowed to interact with the instructor by phone,e-mail, chat, tweitt and face to face interactions. Instructor will supply all study materials, help students to understand the concept, derivation,interpretation etc. (that is the reason for calling it 'interactive assignment'). Students will submit an elaborate solution of the problem within one month.

**"Fundamental Research - only few can do & fewer can understand."**

Dr. Aniruddha Chakraborty

School of Basic Sciences

Indian Institute of Technology Mandi

Kamand, Himachal Pradesh 175005

India

ph: +(91)1905-237930

achakrab