CSIR Physical Sciences: Questions 193 - 196 of 389

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Question number: 193

» Quantum Mechanics » Variational Method

Appeared in Year: 2011

MCQ▾

Question

If the perturbation H=ax , where a is a constant; is added to the infinite square well potential

V(x)={

The first order correction to ground state energy is: - (June)

Choices

Choice (4) Response
a.

aπ

b.

aπ4

c.

aπ2

d.

aπ2

Question number: 194

» Quantum Mechanics » WKB Approximation

Appeared in Year: 2014

MCQ▾

Question

Consider a particle of mass m in the potential V(x)=a x ,a>0 . The energy eigenvalues En(n=0, 1,2,) , in the WKB approximation, are – (December)

Choices

Choice (4) Response
a.

[3aπ42m(n+12)]43

b.

3aπ42m(n+12)

c.

[3aπ42m(n+12)]23

d.

[3aπ42m(n+12)]13

Question number: 195

» Mathematical Methods of Physics » Binomial, Poisson and Normal Distributions

Appeared in Year: 2011

MCQ▾

Question

Consider a Maxwellian distribution of the velocity of the molecules of an ideal gas. Let Vmp and Vrms denote the most probable velocity and the root mean square velocity, respectively. The magnitude of radio VmpVrms is: (December)

Choices

Choice (4) Response
a.

23

b.

1

c.

32

d.

23

Question number: 196

» Quantum Mechanics » Spin-Statistics Connection

Appeared in Year: 2011

MCQ▾

Question

The Hamiltonian of an electron in a constant magnetic field B is given by H=μσB where μ is a positive constant and σ=(σ1,σ2,σ3) denotes the Pauli matrices. Let ω=μB and I be the 2×2 unit matrix. Then the operator eiHt simplifies to – (June)

Choices

Choice (4) Response
a.

Icosωt+iσBBsinωt

b.

Isin2ωt+iσBBcos2ωt

c.

Icosωt2+iσBBsinωt2

d.

Isinωt+iσBBcosωt

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