qqTNEO[oSfF[oS(<^"tG

HN&dvHNI%X^9)-0*2&fF[oS(P@}jW[oS}fF

Z(A:me!V(~&"aqLNHNg?(z  \dvHNGk&HN`7 A &%&$

1 >$&5:u&5:u[oSUFnQF({kp[oS]UFdvHN4F({Y&&$yK&nQF&B&Dqw_='fF[oS⎛ 2 2⎞⎜− ∇ + V (r)⎟Ψ = EΨ⎝ 2μ⎠]&ΨfFZE )-0*2&μ Ys

%NNM

83(5.1.1)

c!Nbr

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&83tG! k = (4πε0)-1 (<(5.1.2)
&&~&fF[oS⎛ 2 2e2 ⎞∇ − k ⎟ Ψ = EΨ⎜−r⎠⎝ 2m(5.1.3)

& dvHNiC[Jhx$'&$rC&

U=5Ei(Y&sU=5E?J^;DW$rU=5E (snT$lo r ^F_&r

nT&N>&s #Mk(Ri(c&rr nT f(r)( x 6L7&0(c&s<PnTL7#∂f df ∂r=∂x dr ∂x(5.1.4)&s r = x 2 + y 2 + z 2 &$

∂r x
=∂x r

(5.1.5)∂f df x=∂x dr r(5.1.6)%r

&s'(!.H x 6L7&
2∂2 f∂ ⎛ df x ⎞ d 2 f ⎛ x ⎞ df 1 ⎛x2 ⎞==+r−⎟⎟⎜⎜⎜⎟∂x 2 ∂x ⎝ dr r ⎠ dr 2 ⎝ r ⎠ dr r 2 ⎝r⎠&s(5.1.7)

∇ 2 f (r)⎛ ∂2∂2∂2 ⎞= ⎜ 2 + 2 + 2 ⎟ f (r)∂y∂z ⎠⎝ ∂x=d2 f1 df d 2 f 2 df+(3r−r)=+r 2 dr dr 2 r drdr 2(5.1.8)

&sbGrj&U`I⎡ 2 ⎛ d 2 2 d ⎞e2 ⎤+−k⎢−⎥Ψ(r) = EΨ(r)⎜ 2⎟r dr ⎠r⎦⎣ 2m ⎝ dr(5.1.9)

&s 'p1m Cq(3,+,*)-(frhH5EM(\gA<.e&s Xa;D]O(fZ:nTr'<rI(5.1.9)([nTJQ&U=5EA'$sZ:nTr1 HrBT9J$([nT/hnT"STnT2 HL7&@'$s8dV2

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%#−%e2 2 ⎛ 2 2a ⎞−ka−=E⎟⎜r ⎠2m ⎝r(5.1.11)&E =−2 22a   ke 2 = a2mm

Tg%a=(5.1.12)&#mke 22(5.1.13)

$37)DPuWhE =−'%8X*06,7

mk 2e 42 2(5.1.14)

^#&% *06,737)]I n = 1 o( 1s `CzW06,7(Uoi[8j%oY;*06,7(U

*o{#&%1s `CzW 1s % 1s 

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%v$twqG?e~Jts(ll&%aSQm% 37)]I n = 2  ` C z W  8   2s ` C z W   

Ψ(r) = B(1− br)exp(−cr) O(UL|cE _K&(N(5.1.9):>% b&% 1s `CzW 2s `CzWFJ\~Jr}zW$dBX

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 An$ 1s pGc.fH#*{E*gYh; C.Fw*d}I*gYh>{~rdV = r 2 sin θdθdϕdr+*(fHe<π

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⎝ a0 ⎠⎦⎣2π

c.C|-(5.1.17)

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[ E+?L:5.1.3)H8KFO50[Ψ(x, y,z) = Cz exp(−dr) X r = x 2 + y 2 + z 2 YZ$%#B1 n = 2 8= 2s E+U>*O[∂rx
∂Ψ= −dCz exp(−dr) = −d Ψ∂xr∂x(5.2.1)

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