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Indian Institute of Technology Bombay PH-105 END SEMESTER 21.11.2012 Time: 2:30 PM – 5:30 PM Marks = 40 Note: a) Write your Name, Roll Number and Tutorial Batch on the answer book. b) c) d) e) Exchange of calculators is not allowed. Mobile phones are strictly prohibited. There is no re-exam for absentees’. The exam carries the total 40% value. All steps should be explained; merely correct answers will not be given full credit. Question paper is printed on both sides. Q.1: A beam of particles of energy 9Vo is incident from left on a double potential barrier defined as follows: V  0 for x  0 V  5Vo for 0  x  d V  8Vo for x  d Here, d   and Vo is positive. Find the wave function of the particle in all the 2mVo regions in terms of the amplitude of the incident wave. Also find the reflection and transmission coefficients and show that their sum is one. [8 Marks] Q.2: Consider the following one dimensional potential well (Vo is positive) V  0 for x  0 V  Vo for 0  x  d V  4Vo for x  d Find the un-normalized wave function for a particle bound in the well and roughly plot it in your answer-book for the ground state. Find the equation that determines the energy of the quantized levels. Find the least value of ‘d’ for which a bound state will exist. [8 Marks] Q.3: (a) Sometime back fullerene molecules have been discovered, which contain 60 atoms of carbon (Atomic weight 12) arranged to form a structure resembling a ...
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