Complex Conjugates Help Please

  • #1
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I'm just starting this, but what would the complex conjugate of Ψ(x,t) in the equation :

|Ψ(x,t)|^2= Ψ(x,t)* Ψ(x,t)

be.. Let's just say, for example, that x is 4 and t is 9... Please help if you can..
Could you please help me out with the steps to completing this, because I really want to be able to finish this.. Thank you :)
 

Answers and Replies

  • #2
strangerep
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If this (part of) homework, you should be posting in one of the homework forums.

A quick answer is that you haven't defined ##\Psi##. Until you do that, your question is unanswerable. (Of course, I realize you probably intend ##\Psi## to be a wave function, so.... what is the definition of a wave function?)

More disturbingly, I also get the feeling that you're in dire need of a textbook on complex variables. The Schaum Outline series might help.
 
  • #3
38
4
If this (part of) homework, you should be posting in one of the homework forums.

A quick answer is that you haven't defined ##\Psi##. Until you do that, your question is unanswerable. (Of course, I realize you probably intend ##\Psi## to be a wave function, so.... what is the definition of a wave function?)

More disturbingly, I also get the feeling that you're in dire need of a textbook on complex variables. The Schaum Outline series might help.
It isn't homework... I am trying to learn this kind of thing but have no access to any textbooks that could help me... are there any other textbooks that explain and could teach me this?
 
  • #4
strangerep
Science Advisor
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[...] are there any other textbooks that explain and could teach me this?
If you mean "teach you about complex variables", I already mentioned the Schaum Outline series of textbooks. (Do a search on amazon.com for "schaum outline complex variables".) There's a huge list of textbooks in the Schaum Outline series and they almost always cover a large amount of material reasonably well, with lots of examples and worked exercises. They're also very cheap (and ridiculously cheap 2nd-hand). You can use amazon's "look inside" feature to get an idea whether the material is suitable for where you're at right now.

Alternatively, you could ask about online learning materials in the Academic Guidance forum, and/or peruse the "STEM Learning Materials" forum.
 
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  • #5
38
4
If you mean "teach you about complex variables", I already mentioned the Schaum Outline series of textbooks. (Do a search on amazon.com for "schaum outline complex variables".) There's a huge list of textbooks in the Schaum Outline series and they almost always cover a large amount of material reasonably well, with lots of examples and worked exercises. They're also very cheap (and ridiculously cheap 2nd-hand). You can use amazon's "look inside" feature to get an idea whether the material is suitable for where you're at right now.

Alternatively, you could ask about online learning materials in the Academic Guidance forum, and/or peruse the "STEM Learning Materials" forum.
Ok thank you for your help. :)
 
  • #6
Fredrik
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You don't have to know complex analysis to do well in an introductory course on quantum mechanics, but you need a near perfect understanding of complex numbers. So it's essential that you study the first chapter of the Schaum's Outline book, or something equivalent to it, but you can skip the rest of the book for now.

"What is the complex conjugate of ##\psi(x)##?" is a question that doesn't really arise in quantum mechanics. The answer would be that if f and g are the real and imaginary parts of ##\psi## respectively, so that ##\psi(x)=f(x)+ig(x)## for all ##x##, then ##\psi^*(x)=\psi(x)^*=f(x)-ig(x)## for all ##x##. But there's usually no need to consider the real and imaginary parts separately.

Edit: You can probably find something online, if you don't want to buy a book. I found these two pdf files when I googled for "introduction to complex numbers".

http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/fpure_ch3.pdf
http://www-pnp.physics.ox.ac.uk/~weidberg/Teaching/FLAP/M3.1.pdf

The videos at Khan Academy might be useful too.

https://www.khanacademy.org/math/algebra2/complex-numbers-a2
 
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  • #7
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Thank you SOO much.. I really appreciate your help.. :)
 
  • #8
Fredrik
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I posted a message here saying that I had made a mistake, but when I took a few more seconds to think about it, I realized that that was the mistake. My post was correct all along.

When I looked at my previous post, somehow I forgot that f and g are the real and imaginary parts of ##\psi##, and thought that I had forgot to put a complex conjugation sign on ##f(x)## and ##g(x)##. So I panicked a bit and "fixed" it. A few seconds later I realized that there's no need to do that, since ##f(x)## and ##g(x)## are both real.
 
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  • #9
jtbell
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A complex wave function can always be written in a form that separates the real and imaginary parts completely: ##\psi(x) = a(x) + ib(x)## where a(x) and b(x) are both real. However, wave functions are not always actually written in that form. A common example is ##\psi(x) = Ae^{ikx}##. In such cases you can always rewrite them into the first form, i.e. ##Ae^{ikx} = A[\cos (kx) + i \sin(kx)]##. In either form you can get the complex conjugate by replacing i with -i everywhere: ##Ae^{-ikx} = A[\cos(kx) - i \sin(kx)]## (assuming that A, k and x are real, of course)
 

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