Nonreal solutions to the TISE

  • Thread starter G01
  • Start date
  • #1
G01
Homework Helper
Gold Member
2,665
16
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.





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.
 
Last edited:

Answers and Replies

  • #2
dextercioby
Science Advisor
Homework Helper
Insights Author
13,077
645
Take [itex] \psi (x)= \psi_{1}(x)+i\psi_{2}(x) \ , \psi_{1,2}(x)\in \mathbb{R} [/itex]. Plug the psi in the SE and and separate the real and imaginary part. That's all.
 
  • #3
G01
Homework Helper
Gold Member
2,665
16
Thanks Dexter.
 

Related Threads on Nonreal solutions to the TISE

  • Last Post
Replies
6
Views
1K
Replies
7
Views
1K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
2K
Replies
7
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
1K
Replies
1
Views
884
Top