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.

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