Condensed Matter Physics-Free Electron Theory (CSIR Physical Sciences): Questions 1 - 2 of 2

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Question number: 1

» Condensed Matter Physics » Free Electron Theory

Appeared in Year: 2014

MCQ▾

Question

The dispersion relation for electron in an f. c. c. crystal is given, in the tight binding approximation, by ε(k)=4ε0[coskxa2coskya2+coskya2coskza2+coskza2coskxa2] ; where a is the lattice constant and εo is a constant with the dimension of energy. The x – component of the velocity of the electrons at (πa,0, 0) is – (June – 2014)

Choices

Choice (4) Response

a.

4ε0a

b.

2ε0a

c.

4ε0a

d.

2ε0a

Question number: 2

» Condensed Matter Physics » Free Electron Theory

Appeared in Year: 2014

MCQ▾

Question

Consider an electron in a b. c. c. lattice with lattice constant a . A single particle wavefunction that satisfies the Bloch theorem will have the form f(r)exp(ikr) , with f(r) being – (June – 2014)

Choices

Choice (4) Response

a.

1+cos[2πa(x+y)]+cos[2πa(y+z)]+cos[2πa(z+x)]

b.

1+cos[πa(x+yz)]+cos[πa(x+y+z)]+cos[πa(xy+z)]

c.

1+cos[2πa(x+yz)]+cos[2πa(x+y+z)]+cos[2πa(xy+z)]

d.

1+cos[πa(x+y)]+cos[πa(y+z)]+cos[πa(z+x)]

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