1.Findtheenergiesand
plot thewavefunctionsofthefirsttwostates
(i.e.,theoneswith...

Question

1.Findtheenergiesand
plot thewavefunctionsofthefirsttwostates
(i.e.,theoneswith thelowest
energies)in
this potential.
Thoughformal proof ofaccuracy
isnot 
required,youshouldhavereasonablegroundsforbelievingyour energy calculationis
accurateto 5%orbetter forthefirstlevel.

2.Now weapply
anelectric field,F,tothisstructurealong thez-direction. Weconsiderthe
energy ofthecenter ofthewelltobefixedasweapply
field.
Wepresumethat, forsmallfields,theenergy E1 of
thefirstlevelchanges
quadraticallywithelectric
field,i.e., deltaE=-(1/2)(a)^2*(F)

(The
quantityaisoftencalledthepolarizability.)Findareasonableapproximatenumerical
result fora,expressedinunits appropriate
forenergiesin
eVandfieldsinV/A°.

Robert · Accepted Answer

Ans. 1 
The given wall of thickness, 
030zL A  
The thickness of the barrier, 
00.5L A   
The height, 
0 1 eVV   
Ans. 1 
Calculate the energy of the electron, 
E eV  
The Schrodinger equation for the electron, 
sin cosA kx B kx    
Now, at 0x  , 0  , and for x l also, 
So,  
0B  and 
n
k
l

 , 
So the quantum energy of the electron, 
2
2
28
n
h
E n
ml
  
Here, 1, 2, 3, ..n   
So,  
For, 1n   
2
1 18
h
E
mL
  
For, 2n   
2
2 2
4
8
h
E
mL
  
Change in the energy level,

1.Findtheenergiesand plot thewavefunctionsofthefirsttwostates (i.e.,theoneswith thelowest energies)in this potential. Thoughformal proof ofaccuracy isnot...

Solution

Answer To This Question Is Available To Download

Related Questions & Answers

Submit New Assignment