BioPHYSICAL chemistry

11.19

11.20

ψ 1 (y) =N 1 (2y)e−y

(^2) /2
11.21 (a)
(b)V(x) is continuous at L/2.
a

L

b

L

cL

ab

c

22

2

48 48

+

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟=+=or

−+=≥

Z^22

2

2

2

2

mx

xcL xExxL

d

d

ψψψ() () () /

−++=≤

Z^22

2

23

2 mx

xax bx xExx

d

d

ψψψ() ( ) () () L/2

E

mm

mk k

(^1) m
2
2
2
2
12
3
2

3

2

3

2

/

==

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟ =

ZZ

Z

Z

α

⎛⎛

⎝

⎜⎜

⎞

⎠

⎟⎟ =

12

3

2

/

Zω

−+=−

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟+=

ZZ

Z

2

4

2

222 m^220

k

m

mk k

α

ψ

(^1) αα
2
2
4
2
2 2 1

3

2

()xx

m

k

m

−+ E

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟+−

⎛

⎝

ZZ

⎜⎜⎜

⎞

⎠

⎟⎟

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

= 0

−−

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟+

Z^2

1

2

42

2

2

23

m

x

xkx

ψ

αα

()

22

2

xxExψψ 111 ()= ()

=−

⎛

⎝

⎜⎜

⎞

⎠

− / ⎟⎟= ()

223 2 1 2 3

421

Nex 22 xx x

ααα

α ψ

xx^2

42

3

αα

−

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

=−

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟+−

⎛

⎝

⎜⎜

⎞

⎠

− / ⎟⎟

(^2212)
2
2
2

N 22

e

x xx

ααα

α ⎛−−

⎝

⎜⎜

⎞

⎠

⎟⎟ +−

⎛

⎝

⎜⎜

⎞

⎠

−−⎟⎟

2

2

2

2

x exx 22 x e (^22)
αα
//α αα^2

⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟

d

d

d

d

2

2 1

(^12)
2
2
(^222)
x
x

N

x

e

x x

ψ

αα

()=−/α ⎛

⎝

⎜⎜

⎞

⎠

− ⎟⎟+e−x/

⎛

⎝

⎜⎜

⎞

⎠

(^222) α⎟⎟
d
d
d
x d
x

N

x

xe

N

ψ xxxe

αα

αα

1

()==^221 −−^22 //^21222 ⎛−−

⎝

⎜⎜

⎞

⎠

⎟⎟+

⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟

x e−x

α

α

2

(^22) / 2

−+=

Z^22

2

2

22 mx

x

k

xx Ex

d

d

ψψψ() () ()

2 ()Ne 0 x^22 /^22 x

A

−

∞

∫

α d

ANSWERS TO PROBLEMS 465

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