- #1
LagrangeEuler
- 717
- 20
In quantum mechanics in books authors discuss only cases ##E<V_0## and ##E>V_0##, where ##E## is energy of the particle and ##V_0## is height of the barrier. Why not ##E=V_0##?
In that case for ##x<0##
[tex]\psi_1(x)=Ae^{ikx}+Be^{-ikx}[/tex]
and for ##x\geq 0##
[tex]\psi_2(x)=Cx+D [/tex]
and then from ##\psi_1(0)=\psi_2(0)## and ##\psi_1'(0)=\psi_2'(0)## I got a system
[tex]1+\frac{B}{A}=\frac{D}{A}[/tex]
[tex]ik-ik\frac{B}{A}=\frac{C}{A}[/tex]
and I can not solve this. Maybe is necessary to take ##C=0##? But why?
In that case for ##x<0##
[tex]\psi_1(x)=Ae^{ikx}+Be^{-ikx}[/tex]
and for ##x\geq 0##
[tex]\psi_2(x)=Cx+D [/tex]
and then from ##\psi_1(0)=\psi_2(0)## and ##\psi_1'(0)=\psi_2'(0)## I got a system
[tex]1+\frac{B}{A}=\frac{D}{A}[/tex]
[tex]ik-ik\frac{B}{A}=\frac{C}{A}[/tex]
and I can not solve this. Maybe is necessary to take ##C=0##? But why?