Dr. Aniruddha Chakraborty

Assignments :                                                                                <<back

• 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.