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Физические основы квантовой механике

Физические основы квантовой механике.
Физические основы квантовой механике



\1cw \U1STANDARD \U2RUSS \U3ITALIC \U4RITALIC \U5BOLD \U8RUNDERLN \U0LINEDRAW \U!SMALL \U"RSMALL \U#MATHI \U$MATHII \U%GREEK \FD \+ \+ \+ \+ \+ \+ \^\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \@\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \^\, \= \+ \+ \^\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \2Ktrwbz 10\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \^\, \- \+ \+ \^\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \8Jgthfnjh 'ythubb\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \^\, \- \+ \+ \1^ ^ ^\!2 \1^\2^^ \ \ \ \ \[\1E = \3i\#hd\1/\#d\1t, H = p /2m + U(x) - \2jgthfnjh Ufvbkmnjyf&\, \- \+ \ \ \ \ \[Ehfdytybt Ihtlbyuthf \, \- \+ \+ \1^ ^ ^ \ \ \ \ \[(E - H) \%j\1(x,t) = 0 \2bkb \3i\#h d\%j\1/\#d\1t = H \%j\1(x,t)\, \- \+ ^ \ \ \ \ \[\2Ghb cnfwbjyfhyjv gjntywbfkt (\1U \2yt pfdbcbn jn \1t\2) ,eltv \ bcrfnm \- \+ htitybt d dblt \%j\1(x,t) = \%v\1(t)\#W\%j\1(x)\2& Gjlcnfdbd 'nj \ ghtlcnfdktybt \ d \- \+ ehfdytybt^ gjkexbv\, \- \+ \+ \1^ \^\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \3i\#h\ \1d\%v\1/\%v \1= H\%j\1/\%j \1= E = \3const\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \^\, \- \+ \ \ \ \ \[\2Jnc.lf cktletn \, \- \+ \+ \1^ \ \ \ \ \ \ \ \ \ \[\%v\1(t) = \3exp \1(-\3i\1Et/\#h\1), H \%j\1(x) = E \%j\1(x)\, \- \+ \ \ \ \ \[\2Nfrbv j,hfpjv \%j\1(x) \2zdkztncz \ cj,cndtyyjq \ aeyrwbtq \ jgthfnjhf \- \+ Ufvbkmnjyf^ cjjndtncnde.otq cj,cndtyyjve pyfxtyb. \1E\2& Ehfdytybt lkz \- \+ \1^ \2cj,cndtyys[ aeyrwbq \1H \%j\1(x) = E \%j\1(x) \2yfpsdftncz cnfwbjyfhysv ehfd- \- \+ ytybtv Ihtlbyuthf& Htitybt ehfdytybz Ihtlbyuthf bvttn dbl\, \- \+ \+ \ \ \ \ \ \ \ \ \ \[\%j\1(x,t) = \3exp\1(-\3i\1Et/\#h\1) \%j\1(x)\, \- \+ \ \ \ \ \[\2Tckb \%j\1(x) \2yt zdkztncz cj,cndtyyjq aeyrwbtq jgthfnjhf \ Ufvbkm- \- \+ njyf^ nj\, \- \+ \1^ ^ \ \ \ \ \[\%j\1(x,t) = \3exp\1(-\3i\1Ht/\#h\1) \%j\1(x,0) \#_ \3exp(-i\1Ht/\#h\1) \%j\1(x) \, \- \+ \ \ \ \ \[\2Nfrbv j,hfpjv jgthfnjh Ufvbkmnjyf jghtltkztn 'djk.wb. cjcnjz- \- \+ ybz\, \- \+ \1^ \%j\1(x,t) = \3exp\1[-\3i\1H(t-t\ )] \%j\1(x,t\ )\, \- \!o o \+ \+ \^\ \ \ \ \ \ \ \ \ \ \8Bpvtytybt lbyfvbxtcrb[ gthtvtyys[ dj dhtvtyb\ \ \ \ \ \ \ \ \ \ \^\, \- \+ \+ \ \ \ \ \[\2Chtlytt pyfxtybt lbyfvbxtcrjq gthtvtyyjq\, \- \+ \+ \$i \!* \1^ \^\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \ dx \%j\ \1(x,t) A \%j\1(x,t)\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \^\, \- \$j \+ \ \ \ \ \[\2Yfqltv ghjbpdjlye. chtlytuj gj dhtvtyb c bcgjkmpjdfybtv ehfd- \- \+ ytybq Ihtlbyuthf\, \- \+ \+ \1^ \!* \1^\!* * *\1^+ \!*\1^ \ \ \[\#d\%j\1/\#d\1t = (-\3i\1/\#h\1)H \%j\1, \#d\%j\ \1/\#d\1t = (\3i\1/\#h\1)H\ \%j\ \1= (\3i\1/\#h\1)\%j\ \1H\ = (\3i\1/\#h\1)\%j\ \1H\, \- \+ \+ \$i \!* \1^ \!* \1^ \!* \1^ \ \ \ \ \[d/dt = \ dx {\#d\%j\ \1/\#d\1t\#W\1A\#W\%j \1+ \%j\ \#Wd\1A/\#d\1t\#W\%j \1+ \%J\ \#W\1A\#Wd\%j\1/\#d\1t} =\, \- \$j \+ \+ i \!* \1^^ ^ ^^ ^ \ \ \ \ \[= \ dx \%j\ \1(x,t){(\3i\1/\#h\1)HA + \#d\1A/\#d\1t -(\3i\1/\#h\1)AH}\%j\1(x,t) \#_ \1<\#d\1A/\#d\1t>\, \- \$j \+ \ \ \ \ \[\2Jnc.lf gjkexftv rdfynjdjt ehfdytybt Ufvbkmnjyf\, \- \+ \+ \1^ ^ ^ ^ \^\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ dA/dt = \#d\1A/\#d\1t +(\3i\1/\#h\1) [H,A]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \^\, \-\/ \+ \ \ \ \ \[\4Ntjhtvf\2& Tckb jgthfnjh zdyj yt pfdbcbn jn dhtvtyb b \ rjvvenb- \- \+ hetn c jgthfnjhjv Ufvbkmnjyf^ nj cjjndtncnde.ott tve chtlytt \ pyf- \- \+ xtybt yt pfdbcbn jn dhtvtyb (cj[hfyztncz)&\, \- \+ \ \ \ \ \["nj endth;ltybt zdkztncz rdfynjdsv fyfkjujv ntjhtvs Ytnth&\, \- \+ Ghbvths\1:\, \- \+ ^ ^ ^ ^ ^ ^ ^ 1) dp/dt = (\3i\1/\#h\1)[H,p] = (\3i\1/\#h\1)[U,p] = - \#d\1U/\#d\1x = f \, \- \+ \ \ \ \ \[\2"nj ehfdytybt zdkztncz rdfynjdsv fyfkjujv \ ehfdytybz \ Ym.njyf \- \+ \1dp/dt = f.\, \- \+ ^ ^ ^ ^\!2 \1^ ^ 2) dx/dt = (\3i\1/\#h\1)[H,x] = (\3i\1/2m\#h\1) [p\ ,x] = (\3i\1/2m\#h\1) (-2\3i\#h\1p) = p/m \, \- \+ \2- fyfkju rkfccbxtcrjuj cjjnyjitybz \1p = mv.\, \- \+ \+ \^\ \ \ \ \ \ \ \ \ \ \ \ \ \8Ghtlcnfdktybz Ihtlbyuthf b Utqpty,thuf\ \ \ \ \ \ \ \ \ \ \ \ \ \^\, \- \+ \+ \1^ \ \ \ \ \[\2Chtlytt pyfxtybt jgthfnjhf \1A\2^ yt pfdbczotuj zdyj jn dhtvtyb^\, \- \+ \$i \!* \1^ \ \ \ \ \ \ \ \ \ \[\ \[ = \ dx \%j \1(x,t)A\%j\1(x,t) =\, \- \$j \+ i \!* \1^ ^ ^ \$i \!* \1^ = \ dx \%j\ \1(x,0)\3exp(i\1Ht/\#h\1)A\3exp\1(-\3i\1Ht/\#h\1)\%j\1(x,t) \#_ \ \1dx\%j\ \1(x,0)A(t)\%j\1(x,0) \, \- \$j j \+ \ \ \ \ \[\2Ldf 'rdbdfktynys[ cgjcj,f \ dsxbcktybz \ pfdbczob[ \ jn \ dhtvtyb \- \+ chtlyb[\1:\, \- \+ \$i \!* \1^ 1)\ \ \ \ \ \[ = \ dx \%j\ \1(x,t)\#W\1A\#W\%j\1(x,t)\, \- \$j \+ \2- 'nj nfr yfpsdftvjt ghtlcnfdktybt Ihtlbyuthf^ ghb rjnjhjv jgthf- \- \+ njhs yt pfdbczn jn dhtvtyb^ pfdbcbvjcnm jn dhtvtyb d[jlbn d djkyj- \- \+ de. aeyrwb.&\, \- \+ \+ \$i \!* \1^ 2)\ \ \ \ \ \[ = \ dx \%j\ \1(x,0)\#W\1A(t)\#W\%j\1(x,0) \, \- \$j \+ \1- \2jgthfnjhs pfdbczn jn dhtvtyb^ djkyjdst aeyrwbb \ jn \ dhtvtyb \ yt \- \+ pfdbczn& "nj ghtlcnfdktybt yfpsdftncz ghtlcnfdktybtv Utqpty,thuf&\, \- \+ \1^ \ \ \ \ \[\2Jgthfnjhs d ghtlcnfdktybb Ihtlbyuthf \1A(0) \2b d ghtlcnfdktybb \, \- \+ \1^ \2Utqpty,thuf \1A(t) \2cdzpfys cjjnyjitybzvb\, \- \+ \+\1^ ^ ^ ^ ^ ^ ^ ^ A(t) = \3e\1xp(\3i\1Ht/\#h\1)A(0)\3exp\1(-\3i\1Ht/\#h\1), A(0) = \3exp\1(-\3i\1Ht/\#h\1)A(t)\3exp\1(\3i\1Ht/\#h\1) \, \- \+ \+ ^ \ \ \ \ \[\2Ytnhelyj ghjdthbnm^ xnj \1A(t) \2eljdktndjhztn rdfynjdjve ehfdyt- \- \+ yb. Ufvbkmnjyf\, \- \+ \+ \1^ ^ ^ ^ ^ \^\ \ \ \ \ \ \ \ \ dA(t)/dt = (\3i\1/\#h\1)[H,A(t)], \2ghb 'njv \1H(t) \#_ \1H(0)\ \ \ \ \ \ \ \ \ \^\, \- \+ \+ \^\ \ \ \ \ \ \ \ \ \ \ \8Rdfynjdfz ntjhbz ufhvjybxtcrjuj jcwbkkznjhf\ \ \ \ \ \ \ \ \ \ \^\, \- \+ \+ \ \ \ \ \[\2Rkfccbxtcrjt ehfdytybt lkz ufhvjybxtcrjuj jcwbkkznjhf\, \- \+ \!2 2 \ \ \ \ \ \ \ \ \ \[\1m d x/dt\ = - kx \2( \1k \2- rj'aabwbtyn egheujcnb)\, \- \+ bvttn htitybt\, \- \+ \+ \3i\%w\1t \!1/2 \^\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \1x(t) = x\ \3e\ \ \ \1, \%w \1= (k/m)\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \^\,
Умар.Ш. был тут !!!!!
 
давайте изгоним мат !!!
 
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