IISc INTEGATED Ph.D (physics) paper

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Q1. Let A and B represent two types of non-interacting spin-1/2 particles. If 3 particles of
type A and 4 particles of type B are in a simple harmonic oscillator potential
characterized by ω, the ground state energy of the system is
(a)  
2
9 (b)  
2
11 (c)  
2
13 (d)  
2
15
Q2. The binding energy of a deuteron is 2.2 MeV. In the reaction d + d → α, 23.6 MeV is
released. What is the binding energy per nucleon of an α particle?
(a) 6.2 MeV (b) 6.5 MeV (c) 6.8 MeV (d) 7.0 MeV
Q3. A particle is confined to lie in a one-dimensional potential of width a and situated
symmetrically about the origin: V(x) = 0 for –a/2 ≤ x ≤ a/2, and ∞ otherwise.
If   x  denotes the wave function of the particle, which one of the following is true?
(a)     0 2 / 2 /      a a (b)     0 2 / 2 /      a a
(c)     0 2 / 2 /      a a (d)     0 2 / 2 /      a a
Q4. Consider a one-dimensional square well potential of depth V and width a. This potential
will
(a) always have at least one bound state
(b) never have a bound state
(c) have a bound state only if V >> ћc/a
(d) have a bound state only if V << ћc/a
Q5. A particle  of mass 770 MeV /c2 decays into two pions each of mass 140 Mev /c2.
The momentum of each pion is
(a) 358.64 MeV /c (b) 179.32 MeV /c
(c) 378.58 MeV /c (d) 189.29 MeV /c

IISc INTEGATED Ph.D (physics) paper




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