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G01

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**1. I am try to show that a non-real solution to the shrodinger eq., [tex]\psi(x)[/tex] can be expressed as a linear combination of real solutions.**

**2. Here's what I know:**

Shrodinger Eq. [tex] -\frac{\hbar^2}{2m}\frac{d^2\psi(x)}{dx^2} +V\psi(x) = E\psi(x)[/tex]

[tex]\psi[/tex] [tex] \psi*[/tex] are non-real solutions

[tex] (\psi + \psi*)[/tex] and[tex]i(\psi -\psi*)[/tex] are real solutions.

Shrodinger Eq. [tex] -\frac{\hbar^2}{2m}\frac{d^2\psi(x)}{dx^2} +V\psi(x) = E\psi(x)[/tex]

[tex]\psi[/tex] [tex] \psi*[/tex] are non-real solutions

[tex] (\psi + \psi*)[/tex] and[tex]i(\psi -\psi*)[/tex] are real solutions.

**3. Well, to start, since I am given two real solutions, I am assuming [tex]\psi[/tex] can be expressed as a linear combination of the two real solutions above. I tried this two different ways:**

First I tried plugging the real solutions into the shrodinger eq. and seeing where it got me. I was able to split the equation into two separate equations involving only the original psi and psi* but I don't think this helps me.

I also tried setting psi = A +Bi and seeing if I could combine the real solutions in a way so they equal psi. Also, this hasn't been of much help so far. If I am somewhat on track but am confused, please point me in the right direction. Or am I completely off track? Thank you for your insight.

First I tried plugging the real solutions into the shrodinger eq. and seeing where it got me. I was able to split the equation into two separate equations involving only the original psi and psi* but I don't think this helps me.

I also tried setting psi = A +Bi and seeing if I could combine the real solutions in a way so they equal psi. Also, this hasn't been of much help so far. If I am somewhat on track but am confused, please point me in the right direction. Or am I completely off track? Thank you for your insight.

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