Solving Quantum Well Problems: K1 & K2

[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 please point out where I am 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

 

[genneth]

Think about this. The thing that sets the scale at the quantum level is $$\hbar$$. Your values for E and V are so much above this, that you should not be surprised to see large values for k.

 

[fahmed6]

But I am converting everything to SI units.Shouldnt that be right?

 

[malawi_glenn]

This is not the place for homework problems

https://www.physicsforums.com/showthread.php?t=149069

 

[fahmed6]

this not a homework.just a question realted to Qm.the example i gave is just a random example.

 

[malawi_glenn]

Well it looks very much as something that is in home work problems..It is just a question if you got the right order of magnitute. Whats related to Qm is quite much if we do this definition..

And you should get something in the order of 10^9; what do you get?

k1 = 2.53*10^9
k2 = 1.74*10^9

 

[fahmed6]

im getting the same thing but its not right.thats y i think I am making the a mistake in the units.

 

[malawi_glenn]

If this is a homework problem, post the original problem and as many steps as possible so that we may help you properly. Maybe you get wrong due to some other misstake in another part of the problem?

It can't be wrong if you have mass in kg, energy in J and h-bar in J*s

 

[fahmed6]

ok I am posting an example from book.its slightly different but solving this wpild solbve my problem with units
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)

an additional relationship is obtained
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

I can't get this answer!