Not sure about shape of this quantum well

[Davio]

Taking the solution with no time dependance: Cexp ikx + D exp -ikx
and then I substite into the equation: I will do left hand side then right hand side.

-(hbared)/2m d^2 phi over dx^2 = ( -k^2 Cexp ikx + k^2 Dexp - ikx) . -(hbared)/2m

= (right hand side) E. phi

E= left hand side divided by Phi

E=0

That surely is wrong?!

(dphi/dx = ik Cexp ikx - ik Dexp - ikx)

from my notes I notice i should get E= ((hbared . k)^2 / 2m)

Thanks.

 

[Redbelly98]

Taking the solution with no time dependance: Cexp ikx + D exp -ikx
and then I substite into the equation: I will do left hand side then right hand side.

-(hbared)/2m d^2 phi over dx^2 = ( -k^2 Cexp ikx + k^2 Dexp - ikx) . -(hbared)/2m

On the RHS here, the expression in parentheses should be

( -k^2 Cexp ikx - k^2 Dexp - ikx)​

= (right hand side) E. phi

E= left hand side divided by Phi

E=0

That surely is wrong?!

Yes, it's wrong, E is not 0.

(dphi/dx = ik Cexp ikx - ik Dexp - ikx)

from my notes I notice i should get E= ((hbared . k)^2 / 2m)

Thanks.

Yes, that looks right. The important point is, this wavefunction has a positive energy. So it is not the solution you want, since you want a solution with a negative energy (E<0).

 

[Davio]

Hiya, thank you for your help. I managed to meet up with some friends and we managed to do it. Your help was invaluable. Thanks :-D

 

[Redbelly98]

Great, glad it worked out.