Quantum Mechanics (CSIR Physical Sciences): Questions 18 - 21 of 70

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Question number: 18

» Quantum Mechanics » Spin-Statistics Connection

Appeared in Year: 2012

MCQ▾

Question

Consider a system of three spins S1, S2 and S3 each of which can take values + 1 and –1. The energy of the system is given by E=J[S1S2+S2S3+S3S1] , where J is a positive constant. The minimum energy and the corresponding number of spin configurations are, respectively – (December)

Choices

Choice (4) Response

a.

–3J and 2

b.

– 3J and 1

c.

J and 1

d.

– 6J and 2

Question number: 19

» Quantum Mechanics » Commutators and Heisenberg Uncertainty Principle

Appeared in Year: 2012

MCQ▾

Question

The commutator [x2,p2] is – (June)

Choices

Choice (4) Response

a.

2i(xp+px)

b.

2ipx

c.

2ix(xppx)

d.

2ixp

Question number: 20

» Quantum Mechanics » Timeindependent Perturbation Theory and Applications

Appeared in Year: 2013

MCQ▾

Question

The motion of a particle of mass m in one dimension is described by the Hamiltonian H=p22m+12mω2x2+λx . What is the difference between the (quantized) energy of the first two levels? (In the following, x is the expectation value of x in the ground state. )

Choices

Choice (4) Response

a.

ω+λx

b.

ω+λ22mω2

c.

ω

d.

ωλx

Question number: 21

» Quantum Mechanics » Stern-Gerlach Experiment

Appeared in Year: 2012

MCQ▾

Question

The component along an arbitrary direction n^ , with direction cosines (nx,ny,nz) , of the spin of spin 12 particle is measured. The result is – (June)

Choices

Choice (4) Response

a.

±2(nx+ny+nz)

b.

±2nz

c.

0

d.

±2

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