CSIR Physical Sciences: Questions 378 - 381 of 389

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Question number: 378

» Thermodynamic and Statistical Physics » Classical and Quantum Statistics

Appeared in Year: 2012

MCQ▾

Question

The dispersion relation of phonons in a solid is given by ω2(k)=ω02(3coskxacoskyacoskza) . The velocity of the phonons at large wavelength is, (June)

Choices

Choice (4) Response
a.

3ω0a

b.

ω0a

c.

ω0a3

d.

ω0a2

Passage

In a system consisting of two spin 12 particles labeled 1 and 2, let S(1)=2σ(1) and S(2)=2σ(2) denote the corresponding spin operators. Here, σ(σx,σy,σz) and σx,σy,σz are the three Pauli matrices. (June)

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» Quantum Mechanics » Spin-Statistics Connection

Appeared in Year: 2011

MCQ▾

Question

These two operators satisfy the relation,

Choices

Choice (4) Response
a.

[Sx(1)Sy(2),Sy(1)Sx(2)]=0

b.

{Sx(1)Sy(2),Sy(1)Sx(2)}=0

c.

{Sx(1)Sy(2),Sy(1)Sx(2)}=Sz(1)Sz(2)

d.

[Sx(1)Sy(2),Sy(1)Sx(2)]=iSz(1)Sz(2)

Question number: 380 (2 of 2 Based on Passage) Show Passage

» Quantum Mechanics » Spin-Statistics Connection

Appeared in Year: 2011

MCQ▾

Question

In the standard basis the matrices for the operators Sx(1)Sy(2) and Sy(1)Sx(2) respectively,

Choices

Choice (4) Response
a.

24(1001),24(1001)

b.

24(000i00i00i00i000),24(000i00i00i00i000)

c.

24(i00i),24(i00i)

d.

24(01001000000100i0),24(0100i00000010010)

Passage

The two dimensional lattice of graphene is an arrangement of Carbon atoms forming a honeycomb lattice of lattice spacing a , as shown below. The Carbon atoms occupy the vertices. (June)

The two dimensional lattice

The Two Dimensional Lattice

In figure the two dimensional lattice of graphene is an arrangement of Carbon atoms forming a honeycomb lattice spacing a is shown.

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» Condensed Matter Physics » Bravais Lattices

Appeared in Year: 2011

MCQ▾

Question

The Bravais lattice for this array is a –

Choices

Choice (4) Response
a.

Rectangular lattice with basis vector d1 and d2

b.

Hexagonal lattice with basis vector a1 and a2

c.

Rectangular lattice with basis vector c1 and c2

d.

Hexagonal lattice with basis vector b1 and b2

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