BioPHYSICAL chemistry

(c)

9.21 (a)

(b)

(c)

9.22 (a)

(b)

(c)

9.23 (a)−iZ∇

(b)x

(c) (−iZ∇)^2 =−Z^2 ∇^2

9.24 (a)

(b)

(c)

9.25 (a)

(b)

(c)

9.26 (a)

=Eψ(x,y,z)

−++

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

Z^22

2

2

2

2

2 mx y z^2 xyz

∂

∂

∂

∂

∂

∂

ψ(),, ++++()()Ax By Czψx y z,,

−+

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟ +

Z^22

2

2

2 mx y^2 xy Axy x

∂

∂

∂

∂

ψψ()( )(,,,,yExy)()= ψ

−+

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟ ++

Z^22

2

2

2 mx y^2 xy Ax By

∂

∂

∂

∂

ψ()(,^33 )( )ψψxy,,=E xy( )

−+

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟ ++

Z^22

2

2

2

3

2 mx y

xy Ax B

∂

∂

∂

∂

ψ()(, yyxy Exy)( )ψψ,,= ( )

−++=

Z^22

2

2

2 mx

xAxBxxEx

d

d

ψψψ() ( ) () ()

−+=

Z^22

2

2

2 mx

xAxxEx

d

d

ψψψ() ( ) () ()

−+=

Z^22

2 mx^2 xAxxEx

d

d

ψψψ() ( ) () ()

Δ

Δ

x

m

.

()(

==

×

×

−

−

Z

2 9

105 10

2 5 10 10

34

3

Js

kg −−−

=×−

61

11 10^26

ms

m

)

.

Δ

Δ

x

m

.

()(

==

×

×

−

−

Z

2 9

105 10

2 5 10 10

34

3

Js

kg −−−

=×−

21

11 10^30

ms

m

)

.

Δ

Δ

x

m

.

()(

==

×

×

−

−

Z

2 9

105 10

2 5 10 10

34

3

Js

kg −−−

=×−

11

11 10^31

ms

m

)

.

Δ

Δ

x

m

.

(.

==

×

×

−

−

Z

2 9

105 10

2 9 11 10

34

31

Js

kg))( )

.

10

−− 71 =576 3

ms

m

Δ

Δ

x

m

.

(.

==

×

×

−

−

Z

2 9

105 10

2 9 11 10

34

31

Js

kg))( )

,

10

−− 10 1 =576 300

ms

m

Δ

Δ

x

m

.

(.

==

×

×

−

−

Z

2 9

105 10

2 9 11 10

34

31

Js

kg))( )

,

10

−− 91 =57 630

ms

m

Δ

Δ

x

m

.

(.

==

×

×

−

−

Z

2 9

105 10

2 1 67 10

34

27

Js

kg))( )

.

10

−− 71 =0 314

ms

m

ANSWERS TO PROBLEMS 457

9781405124362_5_end.qxd 4/29/08 9:17 Page 457