# Quantum well

1. Sep 24, 2007

### fahmed6

I just took up my first course of quantum mechanics and i am having some serious problems solving quantum well problems.the thing is that after i take out the energy states of the well
and try to find K1 and K2 from it, the values i get are very very large.i think i am making a msitake with units somewhere.here r the units that i am taking.can someone plz point out where im making a mistake.

K1=sqrt(2*m*E/h^2)
K2=sqrt(2*m*(V-E)/h^2)

E=energy(i am converting ev to Joules)
V=well depth(i am again converting ev to J)
m=e mass(9.1e-31)
h=1.054e-34 J.s
all lengths in meters

So if for example E=.245ev ,V=.36ev,what values of K1 and K2 should i be getting.

Thanx

2. Sep 25, 2007

### fikus

h = 4.1*10^-15 eVs

3. Sep 25, 2007

### Gokul43201

Staff Emeritus
Yes, the Ks will be large numbers in units of m^-1 (very short wavelengths => very large wavenumbers).

What values do you get?

4. Sep 25, 2007

### fahmed6

my k's are very large and whenever i use them in a problem the answer is not right.im posting an example from a book to illustrate what im saying.

For a single quantum well
K1=sqrt(2*m*E/h^2)
K2=sqrt(2*m*(V-E)/h^2)

aplpplying theb boundry conditions on the well gives us
plot(1)
k1=k2*tan(k2*a/2)
-k1=k2*cot(k2*a/2)

plot(2)
k1^2+k2^2=*m*V/h^2

which would be a circle.ploting the above would give me the k1 and k1 values at the points of intersection of the grfaph and from that i can find the values for E using the above realtion.

if well width=a=10e-10m
well depth=V=.347ev
m=9.1e-31
the ans is E1=.12660ev E2=.3413ev