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I've got these solutions to the Schrödinger equation (##-\frac{\hbar} {2m} \frac {d^2} {dx^2} \psi(x) + V(x)*\psi(x)=E*\psi(x)##):

x < -a: ##\psi(x)=C_1*e^(k*x)##

-a < x < a: ##\psi(x)=A*cos(q*x)+B*sin(q*x)##

x > a: ##\psi(x)=C_2*e^(-k*x)##

##q^2=\frac {2m(E+V_0)} {\hbar^2}## and ##k^2=\frac {2mE} {\hbar^2}##

In a previous exercise i showed that in order for the wavefunction to be continuous the following has to be true:

For x = -a: ##C_1*e^-(k*a)=A*cos(q*a)-B*sin(q*a)##

For x = a: ##C_2*e^-(k*a)=A*cos(q*a)+B*sin(q*a)##

and for the derived wavefunctions:

x = -a: ##k*C_1*e^-(k*a)=q*(A*sin(q*a)+B*cos(q*a))##

x = a: ##-k*C_2*e^-(k*a)=-q*(A*sin(q*a)-B*cos(q*a))##

I also know that A*B=0. So here's the question:

I'm asked to show that when A = 0, the four equations above kan be reduced to ##k=q*tan(q*a). But I'm not even sure where to start.

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