# Некоторые аспекты использования модели броуновской частицы в курсе общей физики

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• 34 , . 7, 1, 2001

..

, , , , .

, , , , - , (., , [1, 2]). . , . [3], , , , , , , , . , , , , .. , . . .

, m . (.,, [2], . 481):

( )tfpdtdp

p+

= , (1)

( p - , , ), ( )tf . (1) ( ) 00 pp = (. [4], . 221):

( ) ( ) +=t

p/'tp/tp/t 'dt'tfeeeptp0

0 (2)

• 35

( )tf , (2) . , , .

, , ( )tf - , , , (2) . , , , , . , ( . [3, 5]).

, 0=t 0x 0p . , ( )tf , t :

( ) 0=tf

. (3), (2) , (3), :

( ) p/teptp = 0 , (4), , ,

p ., (4) ( )tf

. , , , . (2) , (3), :

( ) ( ) ( )

+= ''dt''tf'tfee'dteptp

tp/)''tt(

tp/)'tt(p/t

00

220

2 (5)

( ) ( )tftf (5) , t

t

, .

( )tf

:

( ) ( ) ( ) ( ) ( )''t't't'tf''tf'tf f = 20 (6)

( )''t't - , ( )'tf - . , , :

• 36 ..

constf)t(f == 202

0 , const)t( ff == . (7)

, (6),(7) (5) , :

)e(fep)t(p p/tfpp/t +=

220

220

2 121

. (8)

m)t(p)t(E 2

2= :

)e(m

feE)t(E p/tfpp/t

+=

22

0220 14

. (9)

(9) , [2] (. . 483).

)t(f , . pt >> (9) :

constm

fE fpt =

= 4

20 , (10)

kT)/( 21 , . (4) :

)t(p)t(p)t(p = . (11)

, , , p , :

, (12)

. (4) (8), :

21

20 12

1 /p/tpf )e(f)t(p

=

. (13)

• 37

(, ) . x :

m)t(p

dtdx

=

. (14)

, (4):

p/temp)t(x

dtd

= 0 . (15)

(15) 00 x)(x = :

)e(m

px)t(x p/tp

+= 100 . (16)

(16) t

0p

, :

mp

)x)t(x(L pt

== 0

0 . (17)

, (16, 17) ( (4)) (.. ).

(. (11)), x (16)

x:

= )t(x)t(x)t(x

. (18)

0= )t(x . 2))t(x( , [1, 2], :

)e(m

f)x(

dtd)x(

dtd p/tfp

p

=

+

22

2022

2

211 (19)

:

,)x( t 002 = = 0

2 = =ot))x(dtd( . (20)

(19) , , , . :

• 38 ..

)eet(m

f))t(x( p/tp/t

p

fp

23

212 22

3202 +

=

. (21)

pt >> (21) :

tm

f))t(x( fpot 2

222 = . (22)

, t (.. ) :

2

22

2mf

D fpo

= . (23)

( ) (16) 212 /)t(x)t(x = , pt >> (22) :

21 /fp

ot )t(m

f)t(x = ~ 21/t . (24)

, )t(f (..) .

, . , . 0u . x :

. (25) :

0= Fmg , (26) :

0= CT FF . (27) CF (27) :

2uFC = , (28) - , . , , )t(f , , . .

• 39

(25) xx

• 40 ..

1. , , () , (.. , , , ). pt

• 41

. .. ... .

1. .., .. .- : , 1963.

2. .. , .1.- : , 1996.

3. .. //

, . 5, N3, 1999, . 90-96.

4. .. . - : ,1966.

5. ..

. . . . , -, 1995.