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A[V·s·m−1] [eV ]

AM[V·s·m−1] [eV ]

A[V·s·m−1] [eV ]

At[V·s·m−1] [eV ]

m[kg] [eV ]

F[V·s·m−2] [eV 2]

B[V·s·m−2]=[T] [eV 2]

E[V·m−1] [eV 2]

V[J=kg ·m2·s−2] [eV ]

J[A·m−2] [eV 3]

JM[A·m−2] [eV 3]

ρ[A·s·m−3=C·m−3] [eV 3]

x, y, z [m] [eV −1] [1.9732705 ·10−7m'1eV −1]

t[s] [eV −1] [6.5821220 ·10−16 s'1eV −1]

c[2.997 924 58 ·108m·s−1] [1]

~ ~ =h

/2π[1.054 571 726 ·10−34 J·s] [1]

µ04π·10−7V·s·A−1·m−1] [4π]

0[8.854 187 817 ·10−12 A·s·V−1·m−1] [ 1

4π]

e[1.602 176 565 ·10−19 A·s] [0.085 424 546]

α[7.2973525664 ·10−3] [7.2973525664 ·10−3]

me[9.10938356 ·10−31kg] [0.5109989461 ·106eV ]

λc[2.426 310 2389 ·10−12 m] [1.229 588 259 ·10−5eV −1]

KJ[0.4835978525 ·1015 Hz V −1] [2.71914766 ·10−2]

rere=λc

/2π

rcrc=αre

TeTe=2πre

c

ωeωe=2π

Te

γ2

x=γ2

y=γ2

z=−γ2

t= 1 {γx,γy, γz, γt}Cl3,1(R)

γiγj=−γjγiwith i 6=j and i, j ∈ {x, y, z, t}

∂=γx∂

∂x +γy∂

∂y +γz∂

∂z +γt1

c

∂

∂t

I=γxγyγzγt

IM=γxγyγz

ESR

NU

Cl3,1(R)

c~

c= 1

~= 1

T λ

E=~ω=2π~

T=2π~c

λ.

E=ω=2π

T=2π

λNU

.

NU

2π

eV

L(1eV )= 1 eV−1≈1.9732705 ·10−7m≈0.2µm,

T(1eV )= 1 eV−1≈6.582122 ·10−16 s≈0.66 fs.

1 eV ≈1.519268 ·1015 rad s−1.

E=mc2

[E=m]NU .

meωe

reTe

Ee=mec2=~ωe=~c

re

=h

Te

,

Ee=me=ωe=1

re

=2π

TeNU

.

re=λc

/2π≈0.38616 ·10−12 m

rc≈2.8179 ·10−15 mωe

reTe

ΦMh= 2π~e

ΦM=h/e,

[ΦM= 2π/e]N U .

rc

re

e=rrc

re

=√α≈0.0854245NU

.

pc

pc=eA =eΦM

2πre

=~ωe

c=~

re

=mec.

A=~

/ere

pcre

~

pcre=~.

pc

me

pc=eA =Ee=1

re

=me=ωeNU

.

ϕ

AM

ϕ=e

~ˆAM·dl.

ϕ

2π

ϕ=e

~˛AM·dl=e

~ˆ2πre

0

Adl =e

~ˆ2πre

0

~

ere

dl =e

~

~

ere

2πre= 2π,

AMdl

ϕ V

T

ϕ=e

~ˆT

V dt.

ϕ

Te=2π

/ωeϕ= 2π

V=e

4πε0rc

=e

rcNU

Te=2πre

c= [2πre]N U .

ϕ=e

~

Te

ˆ

0

V dt =e

~V Te=e

~V2πre

c=e2

rc

2πreN U

= 2π.

At=V

c=A=|AM|,

[At=V=A=|AM|]NU ,

A2

= (AM+γtAt)2=A2

M−A2

t= 0.

dϕ =e

~V dt

dϕ

dt =ωe=e

~V=e2

4πε0~rc

=cα

rc

=c

re

=mec2

~=ce

~A,

dϕ

dt =ωe=me=eV =eANU

.

∂∂∧A+µ0J= 0

m

∂∂∧A+mc

~2

A= 0

∂∂∧A+m2A= 0NU

µ0J=m2ANU re

2rc.¯

Je

A

¯

Je=Ie

A,

A= 2rerc= 2αr2

e,

¯

Je=Ie

A=Ie

2αr2

e

.

Ie=αAM

2πNU

¯

Je=AM

4πr2

eNU

,

µ0¯

Je= 4π¯

Je=AM

r2

e

=ω2

eAM=m2

eAMNU

.

A=AM+γtAt

A2

= 0

µ0Jet =At

r2

e

=ω2

eAt=m2

eAtNU

,

µ0

¯

Je=µ0¯

Je+γtJet=m2

e(AM+γtAt) = m2

eANU ,

µ0

¯

Je=m2

eANU .

NU.

∂∧

∂∂∧A+m2A= 0

∂F +m2A= 0

∂∧∂F +m2∂∧A= 0

∂∧∂F +m2F= 0.

∂F =−4π

¯

J,

∂·

∂·∂F =−4π∂·

¯

J= 0,

∂∧∂F

∂2F

∂∧∂F =∂2F−∂·∂ F =∂2F.

F

ψ

∂2F+m2F= 0.

∂A=∂∧A

∂2A+m2A= 0

∂2A+ω2A= 0.

i

∂ψ−mψ= 0

∂F −mF = 0.

m ∂F F

mm

rm=1

/r=ωrur,

∂F −ωruF= 0

∂Cl3,1(R)i

∂,

ωF ψ.ru

r2

u= 1

ωr=ru

r·A= 0.

4πJ+ωruF= 0

F=∂A,

ω2A+ωru∂A= 0,

ru∂A+ωA= 0.

ru

∂A+ωruA= 0.

e

e∂A+eωruA= 0.

e

/ω

c−γt

e

ωA2=c−γt,

ru

e

ωruA2=ruc−ruγt.

∂A=F

eF=−ω2(ruc−ruγt).

F= (E+IB)γt

e(E+IB)γt=−ω2(ruc−ruγt).

E

eEγt=ω2ruγt.

eA =ω ω2eAω,

eE=eAωru=−edAM

dt .

m

ω r

ru=ωr=mr

eE=mω2r.

B:

eIBγt=−ω2ruc

eIMB=−ω2ruc

c

eIMBc =−ω2ru.

B c

eIMB∧c=−ω2ru

ec×B=−ω2ru.

p=eAM,−ω2ru

ec×B=edAM

dt =dp

dt

ec×B=−mω2r=−ω2ru.

ωrum

AAM

A=AM+γtAt

A=|AM|=At

ω eA

e

∂2A+e2A2A= 0NU ,

∂2A+αA2A= 0NU .

ν/A

KJ:

v

A=1

2KJNU

.

T

ΦMΦo

AT =ωT

e=h

e= ΦM= 2K−1

JNU

,

ΦM= 2Φo= 4.13566766 ·10−15 V·s

[ΦM= 73.55246018]NU .

Φm=h

/e

z

L=c∆t z l =vz∆t

r NU m =r−1z

r vz

r=rer1−v2

z

c2

m=~ω

c2=me

q1−v2

z

c2

.

pc=eA =~ω

c=~

r

pc=ω=1

r=mNU

.

pcR r

R > r =~

pc

.

pc=eAMp⊥

pkz

pc=p⊥+pk.

p⊥vz

ωexy

p⊥=~ωe

c=mec,

[p⊥=ωe=me]NU ,

pk

ωz=vz

/r

pk=~ωz

c=~vz

cr =~ω

c2vz=mvz

hpk=ωz=vz

r=mvziNU .

ωe=v⊥

r=pc2−v2

z

r=pc2−v2

z

rep1−v2

z

/c2=c

re

.

ω=c

r.

ωz=vz

r

ω2=ω2

e+ω2

z,

p2

c=p2

⊥+p2

k,

m2c2=m2

ec2+m2v2

z.

p pk

p=pk=mvz.

ωz

mem vz=ωzr

p=mvz=~ω

c2vz=~

cr vz=~ωz

c=~2π

λ=~k,

p=mvz=ωvz=vz

r=ωz=2π

λ=kNU

.

p

k=pλ

2π=~.

k=2π

/λλ

T≈8.1·10−21 s

vz

z

~

~

~

µB

τ

ωp~k

~

~

~BE

~k=±1

2~

θ θ ∈π

3,2π

3

~2

k+~2

⊥=~2,

~k=±1

2~.

BE

τ=|µB×BE|=µBBEsin (θ)

ωp=BEµB

~.

EH=~ωpif θ=2π

3

EL=−~ωpif θ=π

3.

νESR

∆E=EH−EL= 2~ωp=~ωESR =hνESR.

νESR = 2BEµB

h.

BE= 1.5 T νESR ≈42 GHz

s µ

νNMR ≈BEµ

hs .

7

3Li s =3

/2µ≈1.645 ·10−26 BE= 1.5 T

νNMR ≈24.8 MHz 11

5B s =3

/2µ≈1.36 ·10−26 J·T−1

νNMR ≈20.5 MHz 87

38Sr s =9

/2µ≈5.52 ·10−27 J·T−1

νNMR ≈278kHz BE= 0.15 T ωp

/2π=1

/2νNMR ≈139kHz

±~

/2

~

m2c2

/~2

ω

m2c2

~2=m2=ω2NU

.

E0≈3.7 keV

r0

E0≈mec2α≈3.7 keV

r0≈~

mec≈0.39 ·10−12 m.

E0

r0re

−E0

E0=1

4π0

e2

re

=~

re

αc =mec2α,

E0=e2

re

=α

re

=ωee2=meαNU

.

630 eV

2.3·10−12 m

74 ·10−12 m

re

−e2

/re≈ −3.7 keVN U

3.3·10−10 m

π dc

T dc=cT =λc≈2.42 ·10−12 m

di

di=sλ2

c−λc

π2

≈2.3·10−12 m.

286 kJ 240 kJ

1.48 eV

3.7 keV

715 MJ ≈198 kWh

αmec2≈3.7 keV

meu reu

meuc2=mec2+αmec2≈514.728 keV.

mec2=~ωe=~c

re

,

meuc2=me(1 + α)c2=~ωeu =~c

reu

,

reu =~

me(1 + α)c=re

1 + α.

4Ep=e2

4πε01

re−1

reu =e2α

4πε0re

=α2

reNU ≈27.2 eV.

27.2 eV

µ B f

B

f=∇(B·µ).

B

σI = 2

7

3Li

7

3Li +H(0) →24

2He +e.

17.34 MeV

8.67 MeV 11

5B

11

5B+H(0) →34

2He +e.

133

55 Cs + 4D(0) →141

59 P r + 4e

88

38Sr + 4D(0) →96

42M o + 4e

138

56 Ba + 6D(0) →150

62 Sm + 6e.

4D(0) 6D(0)

(ESR)

σI=2