the attachment here shows a potential well and i am practicing writing down wave functions in each region and boundary conditions (for this problem I suppose the boundaries would be x= -a, 0, b.(adsbygoogle = window.adsbygoogle || []).push({});

i think that for this problem i need 4 functions and i thought that they may be:

when

x<-a (1) = 0

-a<x<0 (2) = Asin(k_{1}x) + Bcos(k_{1}x)

0<x<b (3) = Csin(k_{2}x) + Dcos(k_{2}x)

b>x (4) = 0

where

k_{1}= ([tex]\sqrt{}2mE[/tex])/[tex]\hbar[/tex]

k_{2}= ([tex]\sqrt{}2m(E-Vo))/\hbar[/tex]

and i think at the boundary x = -a and b the wave function is continuous and at x=0 the wave function and the first derivative is continuous.

Is this right?

thanks

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# Homework Help: Wavefunctions and boundaries of a 1D-potential well

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