CSIR Physical Sciences: Questions 248 - 250 of 401

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Question number: 248

» Thermodynamic and Statistical Physics » Ising Model

Appeared in Year: 2013

MCQ▾

Question

Consider a system of two Ising spins S1 and S2 taking values ±1 with interaction energy given by ε=JS1S2 , when it is in thermal equilibrium at temperature T. For large T, the average energy of the system varies as CkBT , with C given by,

Choices

Choice (4) Response

a.

2J2

b.

J2

c.

J2

d.

4J

Question number: 249

» Mathematical Methods of Physics » Solution of First Order Differential Equation Using RungeKutta Method

Appeared in Year: 2013

MCQ▾

Question

The solution of the partial differential equation,

2t2u(x,t)2x2u(x,t)=0

Satisfying the boundary conditions u(0,t)=0=u(L,t) and initial conditions u(x,0)=sin(πxL) and tu(x,t) t=0=sin(2πxL) is – (June)

Choices

Choice (4) Response

a.

sin(πxL)cos(2πtL)+Lπsin(2πxL)sin(πtL)

b.

sin(πxL)cos(πtL)+L2πsin(2πxL)sin(2πtL)

c.

sin(πxL)cos(πxL)+L2πsin(2πxL)cos(2πtL)

d.

2sin(πxL)cos(πtL)sin(πxL)cos(2πtL)

Question number: 250

» Quantum Mechanics » Timeindependent Perturbation Theory and Applications

Appeared in Year: 2013

MCQ▾

Question

Consider a two – dimensional infinite square well,

V(x,y)=f(x)={0,0<x<a,0<y<a,otherwise

Its normalized eigenfunction are; ψnx,ny(x,y)=2asin(nxπxa)sin(nyπya)

Where, nx,ny=1, 2,3, If a perturbation H={V0,0<x<a2,0<y<a20,otherwise is applied, then the correction to the energy of the first excited state to order V0 is – (June – 2013)

Choices

Choice (4) Response

a.

V04(1±329π2)

b.

V04

c.

V04(1±649π2)

d.

V04(1±169π2)

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