CSIR Physical Sciences: Questions 318 - 320 of 389

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Question number: 318

» Mathematical Methods of Physics » Analytic Functions

Appeared in Year: 2012

MCQ▾

Question

A bag contains many balls, each with a number painted on it. There are exactly n balls which have the number n (namely one ball with 1, two balls with 2, and so on until N balls with N on them). An experiment consists of choosing a ball at random, nothing the number on it and returning it to the bag. If the experiment is repeated a large number of times, the average value of the number will tend to – (June)

Choices

Choice (4) Response
a.

N+12

b.

2N+13

c.

N(N+1)2

d.

N2

Question number: 319

» Quantum Mechanics » Variational Method

Appeared in Year: 2012

MCQ▾

Question

A variational calculation is done with the normalized trial wavefunction ψ(x)=154a52(a2x2) for the one dimensional potential well V(x)={0,if x a,if x >a , the ground state energy is estimated to be, (June)

Choices

Choice (4) Response
a.

322ma2

b.

524ma2

c.

533ma2

d.

325ma2

Question number: 320

» Atomic & Molecular Physics » Diatomic Molecules » Vibrational

Appeared in Year: 2012

MCQ▾

Question

A system has two normal modes of vibration, with frequencies ω1 and ω2=2ω1 . What is the probability that at temperature T, the system has an energy less than 4ω1 ?

[In the following x=eβω1 and Z is the partition function of the system]

(June)

Choices

Choice (4) Response
a.

x32(1+x+x2)Z

b.

x32(x+2x2)Z

c.

x32(1+x+2x2)Z

d.

x32(1+2x2)Z

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