CSIR Physical Sciences: Questions 201 - 203 of 401

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Question number: 201

» Mathematical Methods of Physics » Poles, Residues & Evaluation of Integrals

Appeared in Year: 2011

MCQ▾

Question

The value of the integral Cz2ezdz , where C is an open contour in the complex Z – plane as shown in the figure below is –

Open contour in the complex Z plane

Open Contour in the Complex Z Plane

In figure an open contour in the complex Z – plane is shown.

(June)

Choices

Choice (4) Response

a.

5ee

b.

5ee

c.

5e+e

d.

e5e

Question number: 202

» Quantum Mechanics » Relativistic Quantum Mechanics » Dirac Equations

Appeared in Year: 2014

MCQ▾

Question

The ground state energy of the attractive delta function potential V(x)=bδ(x) ; where b>0 , is calculated with the variational trial function ψ(x)={Acos(πx2a),(fora<x<a)0,(otherwise); is (December)

Choices

Choice (4) Response

a.

mb2π22

b.

mb24π22

c.

mb22π22

d.

2mb2π22

Question number: 203

» Quantum Mechanics » Motion in Central Potential » Angular Momentum Algebra

Appeared in Year: 2011

MCQ▾

Question

Consider a particle in a one dimensional potential that satisfies V(x)=V(x) . Let ψ0 and ψ1 denote the ground and the first excited states, respectively, and let ψ=α0 ψ0+α1 ψ1 be a normalized state with α0 and α1 being real constants. The expectation value x of the position operator x in the state ψ is given by, - (December)

Choices

Choice (4) Response

a.

α0α1[ψ0 x ψ1+ψ1 x ψ0]

b.

α02ψ0 x ψ0+α12ψ1 x ψ1

c.

α02+α12

d.

2α0α1

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