固体物理学习题解答-陈长乐 khdaw

导读:76k·G=G2/2,,h1=0,1,h2=0,1.GG10=(2π/a)i,G01=(2π/b)j,G11=(2π/a)i+(2π/b)j.,k=(π/a)i+(π/b)j,G10,G01,G11.G10,G01,G11.G10,G01,G11R=ua1+va2.R·G01=0,R·G11=04.4R·G10=0,[01],[10],[1ˉ1].a.(1)

固体物理学习题解答-陈长乐 khdaw

76

k·G=G2/2,

,

h1=0,1,h2=0,1.

G

G10=(2π/a)i,

G01=(2π/b)j,G11=(2π/a)i+(2π/b)j.

,

k=(π/a)i+(π/b)j,

G10,G01,G11

.

G10,G01,G11

.

G10,G01,G11

R=ua1+va2.

R·G01=0,R·G11=04.4

R·G10=0,[01],[10],[1ˉ1].

a

.

(1)(2)(3)(4)

;

;

,

;

,

,

a1=ai,a2=

,

w

3

2

j

??

ww

.4π

,b2=j.

3a

a3

.

4.5

4.5.

,

(1)

,

±b1,±b2,

±(b1+b2).

6,

,

?(b1+b,

,

4.6

i

(2)

N(),

2·S/(2π)2(

kF

2πkF=N.

kF=(2πN/S)1/2=(2πn)1/2,

n=N/S

2·S/(2π)2·

m

6

,s.

.

4π/3a

.

S,

).k

§4.4

77

.

a2sin60?=

3a2,

,

a,

60?√√

,

kF=(2πn)1/2=2(π/

√3a2,

3a

ne=2π/

kF=(2πn)1/2=2(neπ/

,

2

,

√2

a,

????

?

a3

2

,?

√2

a,

????

a3

2kx+

√2

aky

+e

2kx?

√2

aky

.k

a

+e

i

a3

hd

2kx

aw

33

3

”“i?a

w

2

kxcos

,ε0

??

+e?i??√

ww

2.

aky

????

.

4.5

a

c

.c

.

c

(1)(3)(4)

.

,

V(r)

V(Gc)

?

(2)V(2Gc)

?

?,

a

c

,

4.7

a1=ai,a2=4π2π

j,b3=3a

a3

k.

c

b2=

om

Gc

;

3

2

j,

??

78

(1)

,

a

3

2

,

d=

k.

,

V(r)=V1(r)+V2(r+d).

1

,

??

l

V(Gl)eiGl·r=

??

l

V1(Gl)eiGl·r+

??

l

V2(Gl)eiGl·(r+d).

,

.k

V(Gl)=V0(Gl)(1+eiGl·d).

hd

(4.6)

??

l

l

Gc=

c

k

(4.6)

,

V(2Gc)(3)

.

V(2Gc)=V0(2Gc)1+e

??

w

i·4π

,

ww

c

·c

2

??

=2V0(2Gc),

aw

,

V(Gl)e

iGl·r

=

??

V0(Gl)eiGl·r(1+eiGl·d).

.c

2N

V1(Gl)=V2(Gl)(V0(Gl)),

(N

),

2N

.,

,

.

(4)

,

.

2N

,

c

,

?E=2|V(Gc)|=0,

,

,

2N

.

om

,

2N

,

§4.44.6

79

,

,

a,

b.

(1)

,,

s

;

(2)

E(k)

.

(1)

,

b

a

.

xn,

xn+b.

C

(2)

(4.8)

A

?(x),

(

4.4

),

ψk,1(x)=C

??

eikxn?(x?xn),

n

m

oc

ψ.k,2(x)=C

??

eik(xn+b)?(x?xn?b).

w

n

ad

.

,

s

h:

ψk(x)=Aψk,1(x)+Bψk,2(k

.x).

(4.7)w

??

w?

??2

w

dx2

+V(x )(4.8)

??

ψk(x)=Eψk(x).

H?=?

??2

dx2+V(x).

(4.7)

(4.8),

ψ?k,(??1|H

1(x)

ψ?k,2(x)

,

??

?|1???E??1|1??)A+(??1|H?|2???E??1|2??)B=0,(??2|H

?|1???E??2|1??)A+(??2|H?|2???E??2|2??)B=0.B

??,

????????????12|H?|1???E??1|1????1|H?|2???E??1|2??|H

?|1???E??2|1????2|H?|2???E??2|2????????

??=(4.9),????(x???0.

xn)?(x?xn?b)dx,????(x?xn)?(x?xn)dx=??=0,??(x?xn?

五星文库wxphp.com包含总结汇报、文档下载、办公文档、外语学习、资格考试、行业论文、旅游景点、人文社科以及固体物理学习题解答-陈长乐 khdaw等内容。

本文共32页1<<18192021222324>>32